homological properties of the perfect and absolute integral closures of noetherian domains for a noetherian local domain r let r be the absolute integral closure of r and let r be the perfect closure of r when r has prime characteristic in this paper we investigate the projective dimension of residue rings of certain ideals of r and r in particular we show that any prime ideal of r has a bounded free resolution of countably generated free r modules also we show that the analogue of this result is true for the maximal ideals of r when r has residue prime characteristic we compute global dimensions of r and r in some cases some applications of these results are given

degreep extensions of an unramified regular local ring of mixed characteristicp abstract we investigate the case of degreep extensions and certain degreep2 extensions of an unramified regular local ringr of mixed characteristicp and show thatr is a direct summand as anr module of those extensions some new examples of normal non cohen macaulay rings are given and a question related to the direct summand conjecture is discussed

majorization for a optimal designs in a regression setting the greatest lower bound for the trace of the covariance matrix of the simple least squares estimator is given based on the idea of majorization the problem raised by n n chan schur convexity for a optimal designs j math anal appl 122 1987 1 6 thus possesses a concise solution

criteria for flatness and injectivity let r be a commutative noetherian ring we give criteria for flatness of r modules in terms of associated primes and torsion freeness of certain tensor products this allows us to develop a criterion for regularity if r has characteristic p or more generally if it has a locally contracting endomorphism dualizing we give criteria for injectivity of r modules in terms of coassociated primes and h divisibility of certain hom modules along the way we develop tools to achieve such a dual result these include a careful analysis of the notions of divisibility and h divisibility including a localization result a theorem on coassociated primes across a hom module base change and a local criterion for injectivity

homological invariants of modules over contracting endomorphisms it is proved that when r is a local ring of positive characteristic phi colon r to r is its frobenius endomorphism and some non zero finite r module has finite flat dimension or finite injective dimension for the r module structure induced through phi then r is regular this broad generalization of kunz s characterization of regularity in positive characteristic is deduced from a theorem concerning a local ring r with residue field of k of arbitrary characteristic if phi is a contracting endomorphism of r then the betti numbers and the bass numbers over phi of any non zero finitely generated r module grow at the same rate on an exponential scale as the betti numbers of k over r

canonical elements in local cohomology modules and the direct summand conjecture one of the objectives of this paper is to show that the usual homological consequences of the existence of big cohen macaulay henceforth c m modules e g the new intersection conjecture of peskine szpiro and roberts and the evans griffith syzygy conjecture follow from the direct summand conjecture when the residual characteristic of the local ring is positive this gives a new and substantially more elementary proof of the standard homological conjectures in case the characteristic of the ring itself is positive and reduces the general case of all these conjectures to one rather down to earth conjecture of course this places the direct summand conjecture in a position of central importance so that it now merits an allout attack some partial results on this problem are given in section 6 the conjecture asserts that a regular noetherian ring r is a direct summand as an r module of every module finite extension ring s 3 r the other main objective of this paper is to formulate and develop a theory of certain canonical elements in the local cohomology of special modules of syzygies neither the modules of syzygies nor the induced maps between them are canonical but the identification between the canonical elements is independent of the choices in particular a canonical element qr e hz syz k is associated see section 3 for details with each ndimensional local ring r m k rings are commutative associative with identity local ring means noetherian ring with a unique maximal ideal the conjecture that qr is nonzero for all local rings r turns out to be equivalent to the direct summand conjecture for a given r an infinite family of cases of the latter implies the former

schur convexity for a optimal designs abstract in a regression setting chan j math anal appl 87 1982 45 50 gave a lower bound for the trace of the covariance matrix of the simple least squares estimate for the case in which this lower bound cannot be reached a sharper lower bound and a necessary and sufficient condition for its attainment are obtained using the idea of schur convexity

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

quasilength latent regular sequences and content of local cohomology abstract the quasilength of a finitely generated module that is killed by a power of a finitely generated ideal i is introduced it is the length of a shortest filtration of the module with factors that are cyclic modules killed by i this notion is then used to define a notion of content for the dth local cohomology module of a ring or module with support in an ideal generated by d elements in the case of a ring which is central this content is a real number between 0 and 1 it is not known whether it is independent of the choice of the d generators nor whether it can change if the generators are replaced by powers in positive prime characteristic it is shown that the content is always 0 or 1 this is an open question in equal characteristic 0 and in mixed characteristic it is conjectured that if the elements form a system of parameters in a local ring of dimension d then the content is 1 this is proved if the ring contains a field in mixed characteristic it is an open question in dimension 3 or more and implies the direct summand conjecture the relationship between the notions of quasilength and content and the property that a sequence of elements can become a regular sequence on a ring or module after base change is explored

on the support of local cohomology we examine the question of whether the support of an arbitrary local coho mology module of a finitely generated module over a noetherian ring with support in a given ideal must be closed in the zariski topology several results giving an armative answer to this question are given in particular we show that the support is closed when the given ideal has cohomological dimension at most two or the ambient ring is local of dimension at most four

on the direct summand conjecture and its derived variant andre recently gave a beautiful proof of hochster s direct summand conjecture in commutative algebra using perfectoid spaces his two main results are a generalization of the almost purity theorem the perfectoid abhyankar lemma and a construction of certain faithfully flat extensions of perfectoid algebras where discriminants acquire all p power roots in this paper we explain a quicker proof of hochster s conjecture that circumvents the perfectoid abhyankar lemma instead we prove and use a quantitative form of scholze s hebbarkeitssatz the riemann extension theorem for perfectoid spaces the same idea also leads to a proof of a derived variant of the direct summand conjecture put forth by de jong

on superheight conditions for the affineness of open subsets in this paper we consider the open complement u of a hypersurface y v a in an affine scheme x we study the relations between the affineness of u the intersection of y with closed subschemes the property that every closed surface in u is affine the property that every analytic closed surface is stein and the superheight of a defining ideal a

koszul homology and syzygies of veronese subalgebras a graded k algebra r has property np if it is generated in degree 1 has relations in degree 2 and the syzygies of order p on the relations are linear the green lazarsfeld index of r is the largest p such that it satisfies the property np our main results assert that under a mild assumption on the base field the cth veronese subring of a polynomial ring has green lazarsfeld index c 1 the same conclusion also holds for an arbitrary standard graded algebra provided c gg 0

initial ideals veronese subrings and rates of algebras abstract let s be a polynomial ring over an infinite field and let i be a homogeneous ideal of s let t d be a polynomial ring whose variables correspond to the monomials of degree d in s we study the initial ideals of the ideals v d i t d that define the veronese subrings of s i in suitable orders they are easily deduced from the initial ideal of i we show that in v d i is generated in degree max reg i d 2 where reg i is the regularity of the ideal i in other words the d th veronese subrings of any commutative graded ring s i has a grobner basis of degree max i d 2 we also give bounds on the regularity of i in terms of the degrees of the generators of in i and some combinatorial data this implies a version of backelin s theorem that high veronese subrings of any ring are homogeneous koszul algebras in the sense of priddy trans amer math soc 152 1970 39 60 we also give a general obstruction for a homogeneous ideal i s to have an initial ideal in i that is generated by quadrics beyond the obvious requirement that i itself should be generated by quadrics and the stronger statement that s i is koszul we use the obstruction to show that in certain dimensions a generic complete intersection of quadrics cannot have an initial ideal that is generated by quadrics for the application to backelin s theorem we require a result of backelin whose proof has never appeared we give a simple proof of a sharpened version bounding the rate of growth of the degrees of generators for syzygies of any multihomogenous module over a polynomial ring modulo an ideal generated by monomials following a method of bruns and herzog

the largest non vanishing degree of graded local cohomology modules abstract this paper gives characterizations for the largest non vanishing degree of the local cohomology modules of a graded ring s in terms of a reduction of s and of the associated graded ring of an ideal i in terms of any reduction of i as a consequence this invariant can be computed explicitly for the associated graded ring of any ideal generated by a d sequence and of ideals having small analytic deviation

some restrictions on the maps in minimal resolutions abstract we show that there are certain restrictions on the entries of the maps in the minimal free resolutions of finitely generated modules of infinite projective dimension over noetherian local rings these restrictions provide a way to slightly improve herzog s characterization of modules of finite projective and injective dimensions in characteristic p 0 we also discuss other homological situations related to these restrictions including previously known results on the existence of free summands in syzygy modules

finite regularity and koszul algebras we determine the positively graded commutative algebras over which the residue field modulo the homogeneous maximal ideal has finite castelnuovo mumford regularity they are the polynomial rings in finitely many indeterminates over koszul algebras this proves a conjecture of avramov and eisenbud we also show that if the residue field of a finitely generated graded algebras has finite regularity then so do all finitely generated graded modules

pure subrings of regular local rings endomorphism rings and frobenius morphisms abstract the aim of this paper is threefold first to prove that the endomorphism ring associated to a pure subring of a regular local ring is a noncommutative crepant resolution if it is maximal cohen macaulay second to see that in that situation a different but morita equivalent noncommutative crepant resolution can be constructed by using frobenius morphisms finally to study the relation between frobenius morphisms of noncommutative rings and the finiteness of global dimension as a byproduct we will obtain a result on wild quotient singularities if the smooth cover of a wild quotient singularity is unramified in codimension one then the singularity is not strongly f regular

a optimality for regression designs abstract use is made of a result of horn amer j math 76 1954 620 630 on the existence of a symmetric matrix with prescribed diagonal elements and eigenvalues a necessary and sufficient condition is then given for the existence of an a optimal design for a regression experiment in the dorogovcev selected transl math statist probab 10 1971 35 41 setting

homology over local homomorphisms the notions of betti numbers and of bass numbers of a finite module n over a local ring r are extended to modules that are only assumed to be finite over s for some local homomorphism r s various techniques are developed to study the new invariants and to establish their basic properties in some cases they are computed in closed form applications go in several directions one is to identify new classes of finite r modules whose classical betti numbers or bass numbers have extremal growth another is to transfer ring theoretical properties between r and s in situations where s may have infinite flat dimension over r a third is to obtain criteria for a ring equipped with a contracting endomorphism such as the frobenius endomorphism to be regular or complete intersection these results represent broad generalizations of kunz s characterization of regularity in prime characteristic

on the associated graded rings of parameter ideals in buchsbaum rings is an invariant 1 a of a not depending on the particular choice of a parameter ideal q of a where i a q and e a denote the length of the amodule a q and the multiplicity of a relative to q respectively this is equivalent to saying that every system a a ad of parameters for a is a weak a sequence i e the equality a ai a i a ai m holds for all 0 i d 1 21 thus every cohen macaulay local ring a is clearly buchsbaum with i a 0 and vice versa in this sense the notion of buchsbaum rings is an extension of that of cohen macaulay rings and is originated in an answer of vogel 29 to a problem of buchsbaum 11 notice that the concept of buchsbaum rings may be canonically generalized to that of buchsbaum modules cf e g 11 221 now let us fix a parameter ideal q of a and let g denote the associated graded ring g a ona q qn of q recall that the ring g is cohenmacaulay if a is so actually g is a polynomial ring over a q in this case then what happens when a is buchsbaum this is a motive problem in the present research and our conclusion is briefly stated

qn like variable storage conjugate gradients both conjugate gradient and quasi newton methods are quite successful at minimizing smooth nonlinear functions of several variables and each has its advantages in particular conjugate gradient methods require much less storage to implement than a quasi newton code and therefore find application when storage limitations occur they are however slower so there have recently been attempts to combine cg and qn algorithms so as to obtain an algorithm with good convergence properties and low storage requirements one such method is the code conmin due to shanno and phua it has proven quite successful but it has one limitation it has no middle ground in that it either operates as a quasi newton code using o n 2 storage locations or as a conjugate gradient code using 7n locations but it cannot take advantage of the not unusual situation where more than 7n locations are available but a quasi newton code requires an excessive amount of storage

regularity of modules over a koszul algebra abstract we prove that every module over a commutative homogeneous koszul algebra has regularity bounded by its regularity over a polynomial ring of which the koszul algebra is a homomorphic image from this we derive a result conjectured by george kempf to the effect that a sufficiently high truncation of any module over a homogeneous koszul algebra has a linear free resolution

homological dimension of skew group rings and crossed products abstract in this paper we study the homological dimension of skew group rings and crossed products a sufficient condition for r g a crossed product to have finite right global dimension is given in terms of crossed products over simple artinian factors of r if r is right fbn and left coherent and g is finite some necessary conditions and sufficient conditions for r g a skew group ring of a finite group over a local or semilocal right noetherian ring to have finite right global dimension are also given then in particular if r is commutative noetherian and g is finite we obtain some equivalent conditions for r g a skew group ring to have finite global dimension using work of aljadeff e aljadeff serre s extension theorem for crossed products j london math soc 44 1991 47 54 these results are extended to polycyclic by finite groups

cohen macaulay properties of ring homomorphisms abstract numerical invariants which measure the cohen macaulay character of homomorphisms r s of noetherian rings are introduced and studied comprehensive results are obtained for homomorphisms which are locally of finite flat dimension they provide a point of view from which a variety of phenomena receive a unified treatment the conceptual clarification and technical versatility of this approach leads among other things to a determination of those homomorphisms which preserve the cohen macaulay character of the rings to the discovery of new classes of homomorphisms with remarkable stability properties and to solutions of some problems on flat homomorphisms raised by grothendieck

regularity over homomorphisms and a frobenius characterization of koszul algebras abstract let r be a standard graded algebra over an f finite field of characteristic p 0 let r r be the frobenius endomorphism for each finitely generated graded r module m let m be the abelian group m with the r module structure induced by the frobenius endomorphism the r module m has a natural grading given by deg x j if x m j p i for some 0 i p 1 in this paper we prove that r is koszul if and only if there exists a non zero finitely generated graded r module m such that reg r m this result supplies another instance for the ability of the frobenius in detecting homological properties as exemplified by kunz s famous regularity criterion the main technical tool is the notion of castelnuovo mumford regularity over certain homomorphisms between n graded algebras the latter notion is a common generalization of the relative and absolute castelnuovo mumford regularity of modules

remarks on non commutative crepant resolutions of complete intersections abstract we study obstructions to existence of non commutative crepant resolutions in the sense of van den bergh over local complete intersections

reduced bass numbers auslander s δ invariant and certain homological conjectures in the category of finitely generated modules over a local cohen macaulay ring with dualizing module one can following auslander buchweitz consider maximal cohen macaulay approximations and hulls of finite injective dimension the former give rise to y and for a gorenstein ring invariants the latter to vd invariants which are in some sense dual this last type of invariant has in the guise of what we call a reduced bass number been encountered in the study of the canonical element conjecture cec by hochster in this paper we establish the basic properties of these invariants some known some not we go on to explore the connection with cec the latter is through linkage seen to imply a fact about delta invariants this in turn shows that cec guarantees the existence of certain maximal cohen macaulay modules over a gorenstein ring

new invariants of noetherian local rings abstract we investigate properties of certain invariants of noetherian local rings including their behavior under flat local homomorphisms we show that these invariants are bounded by the multiplicity for cohen macaulay local rings with infinite residue fields and they all agree with the multiplicity when such rings are hypersurfaces we also show that these invariants are all equal to 2 for a non regular cohen macaulay local ring a if and only if a has a minimal multiplicity provided its residue field is infinite

on the structure of the endomorphism ring of a certain local cohomology module let r m denote an n dimensional gorenstein ring for an ideal i r of height c we are interested in the endomorphism ring b homr hic r hic r it turns out that b is a commutative ring in the case of r m a regular local ring containing a field b is a cohen macaulay ring its properties are related to the highest lyubeznik number l dimkextrd k hic r d dimr i in particular r b if and only if l 1 moreover we show that the natural homomorphism extrd k hic r k is non zero

closure operations that induce big cohen macaulay modules and classification of singularities abstract geoffrey dietz introduced a set of axioms for a closure operation on a complete local domain r so that the existence of such a closure operation is equivalent to the existence of a big cohen macaulay module these closure operations are called dietz closures in complete rings of characteristic p 0 tight closure and plus closure satisfy the axioms we define module closures and discuss their properties for many of these properties there is a smallest closure operation satisfying the property in particular we discuss properties of big cohen macaulay module closures and prove that every dietz closure is contained in a big cohen macaulay module closure using this result we show that under mild conditions a ring r is regular if and only if all dietz closures on r are trivial finally we show that solid closure in equal characteristic 0 integral closure and regular closure are not dietz closures and that all dietz closures are contained in liftable integral closure

on the notion of cohen macaulayness for non noetherian rings abstract there exist many characterizations of noetherian cohen macaulay rings in the literature these characterizations do not remain equivalent if we drop the noetherian assumption the aim of this paper is to provide some comparisons between some of these characterizations in non noetherian case toward solving a conjecture posed by glaz we give a generalization of the hochster eagon result on cohen macaulayness of invariant rings in the context of non noetherian rings

length formulas for the local cohomology of exterior powers in 10 huneke noted a proof due to hochster of the following theorem of angeniol and giusti see 1 let r be a local ring n m and g r r a homomorphism such that grade im g n m l suppose the cokernel n of g has finite length then this length equals the length of r ira g n 2 r ira g by i g we denote the ideal in r generated by the m x m minors of a matrix representing g it is well known see 7 that n m 1 is the maximal possible grade if im g t r therefore r is a cohen macaulay ring of dimension n m 1 we further notice that angeniol and giusti in addition assume r to contain the rational numbers and that the theorem has been known for a long time if m n 9 21 10 17 2 in this paper we shall study the problem of angeniol and giusti in a more general context we start from the dual situation f rm r being a homomorphism which we assume to be injective this is equivalent to grade ira f 1 given a basis x of r m and an orientation 7 on r i e an

on the canonical element conjecture the canonical element conjecture is proved in the following two cases i depth a dim a 1 h a is decomposable ii depth a dim a 1 hm a v is cyclic the equivalence of the c e c and the improved new intersection theorem is also established in h m hochster has assigned a canonical element qa e h syz k with each n dimensional local ring a m k i e commutative noetherian local ring a with a unique maximal ideal m and k a m and has conjectured that 71a 0 for every such a in elementary terms this conjecture means the following h for every free resolution f a8i asi i a k 0 of k and for every system of parameters x1 x of a if 4 is any map of complexes k x a f which lifts the quotient surection a xl x k then 4 kn x a asn is nonzero hochster has shown that the above conjecture henceforth c e c is equivalent to the direct summand conjecture and implies the improved new intersection conjecture which can be stated as follows improved new intersection conjecture let a m be a local ring and f be a finite free complex of finitely generated free modules o fd fo such that hi f has finite length for i 0 and ho f has a nonzero minimal generator v such that avp has finite length then dim r d it is well known that the above conjecture henceforth i n i c implies several other homological conjectures in 1 of this paper we prove that a satisfies c e c a satisfies i n i c 1 4 in proving this we come across in 1 3 another equivalent version of c e c which shows that actually c e c boils down to understanding the relations among the resolutions of homologies of k x a and itself in 2 we study the case when depth a dim a 1 we prove 2 2 that a satisfies c e c in the following cases i when h j1 a v is decomposable this implies hi x a is decomposable ii when h 71 a v is cyclic this implies hi x a v is cyclic received by the editors november 18 1985 1980 mathematics subject classification 1985 revision primary 13h10 the author was supported in part by grants from the national science foundation 1987 american mathematical society 0002 9947 87 1 00 25 per page

lower bounds on projective levels of complexes abstract for an associative ring r the projective level of a complex f is the smallest number of mapping cones needed to build f from projective r modules we establish lower bounds for the projective level of f in terms of the vanishing of homology of f we then use these bounds to derive a new version of the new intersection theorem for level when r is a commutative noetherian local ring

diagonal elements and eigenvalues of a real symmetric matrix abstract a simple and constructive proof is given for the existence of a real symmetric matrix with prescribed diagonal elements and eigenvalues numerically implementable algorithms for constructing such a matrix are discussed

ring homomorphisms and finite gorenstein dimension the local structure of homomorphisms of commutative noetherian rings is investigated from the point of view of dualizing complexes a concept of finite gorenstein dimension which substantially weakens the notion of finite flat dimension is introduced for homomorphisms it is shown to impose structural constraints due to a remarkable equivalence of subcategories of the derived category of all modules an essential part of this study is the development of relative notions of dualizing complexes and bass numbers it is proved that the bass numbers of local homomorphisms are rigid extending a known result for local rings quasi gorenstein homomorphisms are introduced as local homomorphisms that base change a dualizing complex for the source ring into one for the target they are shown to have the stability properties of the gorenstein homomorphism that they generalize 1991 mathematics subject classification primary 13h10 13d23 14e40 secondary 13c15

koszul and local cohomology and a question of dutta for a mathfrak m a local ring we study the natural map from the koszul cohomology module h dim a mathfrak m a to the local cohomology module h dim a mathfrak m a we prove that the injectivity of this map characterizes the cohen macaulay property of the ring a we also answer a question of dutta by constructing normal rings a for which this map is zero

depth for complexes and intersection theorems this paper introduces a new notion of depth for complexes it agrees with the classical definition for modules and coincides with earlier extensions to complexes whenever those are defined techniques are developed leading to a quick proof of an extension of the improved new intersection theorem this uses hochster s big cohen macaulay modules and also a generalization of the depth formula for tensor product of modules properties of depth for complexes are established extending the usual properties of depth for modules

newton like methods with limited storage for the solution of elasto viscoplasticity problems quasi newton and secant newton methods have been successful in solving problems of elasto plasticity in this paper these methods are applied to elasto viscoplastic analyses in an algorithm coupling the global solution for displacement increments with local newton raphson stress iteration at each sampling point the familiar rank two dfp and bfgs methods are generalized to the broyden family of algorithms and this generalization is also used to produce a secant newton algorithm corresponding to hoshino s method consideration is given to the most effective strategy when only a limited number of quasi newton iterates may be stored overwriting re start or continuation in secant newton form results are presented for a tunnelling problem using both plane strain and axisymmetric formulations

the monomial conjecture and order ideals ii abstract let i be an ideal of height d in a regular local ring r m k r m of dimension n and let denote the canonical module of r i in this paper we first prove the equivalence of the following the non vanishing of the edge homomorhpism d ext r n d k ext r n k r the validity of the order ideal conjecture for regular local rings and the validity of the monomial conjecture for all local rings next we prove several special cases of the order ideal conjecture monomial conjecture

a note on the monomial conjecture several cases of the monomial conjecture are proved an equivalent form of the direct summand conjecture is discussed let a m k be a noetherian local ring of dimension n m its maximal ideal and k a rn the monomial conjecture henceforth mc of hochster asserts that given any system of parameters henceforth s o p xi xn of a xix2 xn xv xn bt o hochster proved the conjecture in the equicharacteristic case hi h2 he also established the fact that in the mixed and the positive characteristic cases the direct summand conjecture henceforth dsc and hence mc is equivalent to the canonical element conjecture h12 henceforth cec thus mc occupies a central position in the study of several homological conjectures in i1l hochster pointed out that given any s o p xl xn of a xt xt satisfies mc for t sufficiently large next goto g proved mc for buchsbaum rings and koh proved dsc for degree p extensions k several special cases of cec were proved in di when deptha dima 1 in d2 the following result was established if ji annh j a and j jij2 jr where r dima deptha 0 then xl xn satisfies mc if j xl xn this in turn implies that given any s o p xl xn in a complete local normal domain a xi x2 x3 xt satisfies mc for t 0 we will have several more applications of this result in section 2 we recall that there is no loss of generality in assuming a to be a complete local normal domain in our most recent work we established the validity of cec over i a xa when a is a complete local normal domain and x e mj1 d3 ii any almost complete intersection domain a or any almost complete intersection ring a over which p the mixed characteristic is a non zero divisor d4 iii rings of the form r q where r is a complete gorenstein ring such that the complete local normal domain a is a homomorphic image of r dimr dima and q is the canonical module of a d4 and iv complete local normal domains a for which q is s3 thus mc holds in all the above cases the main results of this paper are arranged in the following way in section 1 first we reduce the study of mc to almost complete intersection rings recall that due to the results mentioned earlier the problem boils down to almost complete intersection rings of depth 0 next we prove the following received by the editors july 20 1996 1991 mathematics subject classification primary 13d02 secondary 13h1 0 this work was partially supported by an nsa grant and an nsf grant 1998 american mathematical society

fontaine rings and local cohomology abstract we use a construction due to fontaine to construct rings with almost vanishing local cohomology from rings of mixed characteristic and discuss the question of using this method to construct almost cohen macaulay algebras over the original ring we also show that the existence of almost cohen macaulay algebras implies the monomial conjecture and give an example to show how this procedure can be carried out in a nontrivial case

noncommutative resolution f blowups and d modules abstract we explain the isomorphism between the g hilbert scheme and the f blowup from the noncommutative viewpoint after van den bergh in doing this we immediately and naturally arrive at the notion of d modules we also find as a byproduct a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

locally complete intersection homomorphisms and a conjecture of quillen on the vanishing of cotangent homology classical deflnitions of locally complete intersection l c i homomor phisms of commutative rings are limited to maps that are essentially of flnite type or at the concept introduced in this paper is meaningful for homo morphisms ri s of commutative noetherian rings it is deflned in terms of the structure of in a formal neighborhood of each point of specs w e characterize the l c i property by difierent conditions on the vanishing of the andre quillen homology of the r algebra s one of these descriptions estab lishes a very general form of a conjecture of quillen that was open even for homomorphisms of flnite type if s has a flnite resolution by at r modules and the cotangent complex l sjr is quasi isomorphic to a bounded complex of at s modules then is l c i the proof uses a mixture of methods from commutative algebra difierential graded homological algebra and homotopy theory the l c i property is shown to be stable under a variety of operations including composition decomposition at base change localization and com pletion the present framework allows for the results to be stated in proper generality many of them are new even with classical assumptions for in stance the stability of l c i homomorphisms under decomposition settles an open case in fulton s treatment of orientations of morphisms of schemes