ramification of local fields with imperfect residue fields we define two decreasing filtrations by ramification groups on the absolute galois group of a complete discrete valuation field whose residue field may not be perfect in the classical case where the residue field is perfect we recover the classical upper numbering filtration the definition uses rigid geometry and log structures we also establish some of their properties

algebras with separating almost cyclic coherent auslander reiten components we prove that the class of artin algebras whose auslander reiten quiver admits a separating family of almost cyclic coherent components coincides with the class of generalized multicoil enlargements of concealed canonical algebras moreover the module category homological properties and the representation type of artin algebras with separating families of almost cyclic coherent auslander reiten components are described

continuity of the radius of convergence of differential equations on p adic analytic curves this paper deals with connections on non archimedean especially p adic analytic curves in the sense of berkovich the curves must be compact but the connections are allowed to have a finite number of meromorphic singularities on them for any choice of a semistable formal model of the curve we define a geometric intrinsic notion of normalized radius of convergence of a full set of local solutions as a function on the curve with values in 0 1 for a sufficiently refined choice of the semistable model we prove continuity logarithmic concavity and logarithmic piece wise linearity of that function we introduce and characterize robba connections that is connections whose sheaf of solutions is constant on any open disk contained in the curve precisely as it happens in the classical case

coherence of certain overconvergent isocrystals without frobenius structures on curves in this paper we will prove the coherence as fancyscript d dagger modules of overconvergent isocrystals on curves which do not contain tame parts at each singular points of the given isocrystal even without frobenius structures in the proof we will construct finite presentations concretely using special differential operators defined by garnier and the decomposition theorem of christol mebkhout

a homological characterization of piecewise hereditary algebras let be a finite dimensional algebra over a field k we will show here that is piecewise hereditary if and only if its strong global dimension is finite

hereditary categories with tilting object let k be an algebraically closed field and h a connected abelian k category which is hereditary that is ext2 vanishes on h assume also that hom x y and ext1 x y are finite dimensional vector spaces over k for all x and y in h we consider such hereditary categories h which in addition have a tilting object t that is an object t such that x ext1 t x 0 fact the factors of finite direct sums of copies of t hereditary categories h with a tilting object t are of special interest in connection with the construction of the class of algebras called quasitilted algbras which was introduced in hrs1 they are by definition the algebras of the form endh t op an important property is that h and endh t op have equivalent bounded derived categories the main examples of such hereditary categories are the category modh of finitely generated modules over a finite dimensional hereditary k algebra h and the category cohx of coherent sheaves on a weighted projective line in the sense of gl1 there are also others derived equivalent to them because of the simple description of the corresponding bounded derived category db h it is possible to give a description of those in the same derived equivalence class see ls h2 it follows from hre that they automatically have a tilting object the quasitilted algebras provide common generalization for the tilted and the canonical finite dimensional algebras note that the tilted algebras are those coming from modh using an arbitrary

sbil nikov hopf bifurcation abstract we derive a 2 parameter poincare map modeling a 3 dimensional vector flow near the codimension 2 point defined by a sil nikov homoclinic orbit to a fixed point undergoing a hopf bifurcation in one parameter regime the map reproduces glendinning and sparrow s results for the sil nikov bifurcation while in another regime it provides new results for a small hopf cycle with a global reinjection mechanism the map is analyzed finding primary homoclinic tangencies to the small hopf cycle parameter dependence of periodic orbits associated with these tangencies is described global behavior of the tube like unstable manifold of the hopf cycle is studied in depth analytically and numerically locating its simplest subsidiary tangencies

finite dimensional dynamical system modeling thermal instabilities we describe a three dimensional dynamical system which is obtained as a pseudo spectral approximation to a free boundary problem modeling solid combustion and rapid solidification and is capable of generating its major dynamical patterns these patterns include a hopf bifurcation followed by a sequence of secondary period doubling and a transition to chaos reverse sequences and sequences followed by shilnikov type trajectories a computer assisted bifurcation analysis uncovers some novel mechanisms of stability exchange the most striking of them is an infinite period bifurcation which resembles the classical shilnikov bifurcation but instead of a funnel shaped spiral along which the period is continually increasing the continuation produced a series of isolas each isola is a closed branch of solutions of roughly the same period and with the same number of oscillations the isolas corresponding to consecutive numbers of low amplitude oscillations about the equilibrium are adjacent to each other and appear to accumulate on a saddle focus homoclinic connection of shilnikov type 2000 elsevier science b v all rights reserved

on the swan conductor in positive characteristic let x be a proper smooth surface over an algebraically closed field of positive characteristic and u be a complement of a simple normal crossing divisor for a smooth l adic sheaf on u deligne proved a formula calculating the euler characteristic of by local invariants kato gave another formula for the euler characteristic in case where is of rank 1 using class field theory in this paper we show that local terms of these formulas coincide admitting certain conjectures for vanishing cycles

attractors in a sbil nikov hopf scenario and a related one dimensional map abstract we study a situation close to the sil nikov hopf bifurcation placing special emphasis on the attractors a model is proposed for the return map to a suitable surface which explains some numerical results concerning a particular physical system the model is quite general and can give reasonable explanations to many other examples later on we introduce a circle map as an additional simplification if the return map is strongly dissipative near the attractor this circle map has very interesting properties it plays a role similar to the logistic map in the case of maps on the interval however it doesn t have the disadvantage of escapes to infinity produced in the logistic map when the parameter is large enough

finite groups of symplectic automorphisms of k3 surfaces in positive characteristic we show that mukai s classication of nite groups which may act symplectically on a complex k3 surface extends to positive characteristic p under assumptions that i the order of the group is coprime to p and ii either the surface or its quotient is not birationally isomorphic to a supersingular k3 surface with artin invariant 1 in the case without assumption ii we classify all possible new groups which may appear we prove that assumption i on the order of the group is always satised if p 11 for p 2 3 5 11 we give examples of k3 surfaces with nite symplectic automorphism groups of order divisible by p which are not contained in mukai s list

analogue p adique du theoreme de turrittin et le theoreme de la monodromie p adique 1 rappel de quelques resultats sur la structure p adique d un point singulier d une equation differentielle 322 2 cas d une pente entiere 327 3 cas d une pente fractionnaire premiere a p 333 4 cas d un rang premier a p 335 5 cas general 339 6 l exemple mx 1 3 343 7 la theorie des modules et l implication dr pst 346

spectrum of a linear differential equation with constant coefficients in this paper we compute the spectrum in the sense of berkovich of an ultrametric linear differential equation with constant coefficients defined over an affinoid domain of the analytic affine line mathbb a 1 an k we show that it is a finite union of either closed disks or topological closures of open disks and that it satisfies a continuity property

radii of convergence and index for p adic differential operators we study the radii of p adic convergence of solutions at a generic point of homogeneous linear differential operators whose coefficients are analytic elements as an application we prove a conjecture of p robba for a certain class of operators concerning the relation between radii of convergence and index on analytic elements we also give an explicit factorization theorem for p adic differential operators based on the radii of generic convergence and the slopes of the associated newton polygon

multivariable varphi gamma modules and locally analytic vectors let k be a finite extension of qp and let gk gal q p k there is a very useful classification of p adic representations of gk in terms of cyclotomic modules cyclotomic means that gal k k where k is the cyclotomic extension of k one particularly convenient feature of the cyclotomic theory is the fact that the module attached to any p adic representation is overconvergent questions pertaining to the p adic local langlands correspondence lead us to ask for a generalization of the theory of modules with the cyclotomic extension replaced by an infinitely ramified p adic lie extension k k it is not clear what shape such a generalization should have in general even in the case where we have such a generalization namely the case of a lubin tate extension most modules fail to be overconvergent in this article we develop an approach that gives a solution to both problems at the same time by considering the locally analytic vectors for the action of inside some big modules defined using fontaine s rings of periods we show that in the cyclotomic case we recover the usual overconvergent modules in the lubin tate case we can prove as an application of our theory a folklore conjecture in the field stating that modules attached to f analytic representations are overconvergent

filtrations de type hasse arf et monodromie p adique one proves the crew tsuzuki p adic local monodromy conjecture for local fields of characteristic p 0

rank one solvable p adic differential equations and finite abelian characters via lubin tate groups we introduce a new class of exponentials of artin hasse type called exponentials these exponentials depend on the choice of a generator of the tate module of a lubin tate group mathfrak g over mathbb z p they arise naturally as solutions of solvable differential modules over the robba ring if mathfrak g is isomorphic to widehat mathbb g m over mathbb z p we develop methods to test their over convergence and get in this way a stronger version of the frobenius structure theorem for differential equations we define a natural transformation of the artin schreier complex into the kummer complex this provides an explicit generator of the kummer unramified extension of epsilon dagger k infty whose residue field is a given artin schreier extension of k t where k is the residue field of k we then compute explicitly the group under tensor product of isomorphism classes of rank one solvable differential equations moreover we get a canonical way to compute the rank one module over epsilon dagger k infty attached to a rank one representation of mathrm gal k t mathrm sep k t defined by an artin schreier character

a p adic local monodromy theorem we produce a canonical filtration for locally free sheaves on an open p adic annulus equipped with a frobenius structure using this filtration we deduce a conjecture of crew on p adic differential equations analogous to grothendieck s local monodromy theorem also a consequence of results of andre and of mebkhout namely given a finite locally free sheaf on an open p adic annulus with a connection and a compatible frobenius structure the module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix

the convergence newton polygon of a p adic differential equation ii continuity and finiteness on berkovich curves we study the variation of the convergence newton polygon of a differential equation along a smooth berkovich curve over a non archimedean complete valued field of characteristic zero relying on work of the second author who investigated its properties on affinoid domains of the affine line we prove that its slopes give rise to continuous functions that factorise by the retraction through a locally finite subgraph of the curve

tilted algebras and short chains of modules we provide an affirmative answer for the question raised almost 20 years ago in reiten et al proc am math soc 117 343 354 1993 concerning the characterization of tilted artin algebras by the existence of a sincere finitely generated module which is not the middle of a short chain

refined characteristic class and conductor formula in this article we prove a conductor formula in a geometric situation which is an analogue of the grothendieck ogg shafarevich formula our approach uses the ramification theory of abbes and saito and relies on tsushima s refined characteristic class

multimodal oscillations in systems with strong contraction one and two parameter families of flows in r 3 near an andronov hopf bifurcation ahb are investigated in this work we identify conditions on the global vector field which yield a rich family of multimodal orbits passing close to a weakly unstable saddle focus and perform a detailed asymptotic analysis of the trajectories in the vicinity of the saddle focus our analysis covers both cases of sub and supercritical ahb for the supercritical case we find that the periodic orbits born from the ahb are bimodal when viewed in the frame of coordinates generated by the linearization about the bifurcating equilibrium if the ahb is subcritical it is accompanied by the appearance of multimodal orbits which consist of long series of nearly harmonic oscillations separated by large amplitude spikes we analyze the dependence of the interspike intervals which can be extremely long on the control parameters in particular we show that the interspike intervals grow logarithmically as the boundary between regions of sub and supercritical ahb is approached in the parameter space we also identify a window of complex and possibly chaotic oscillations near the boundary between the regions of sub and supercritical ahb and explain the mechanism generating these oscillations this work is motivated by the numerical results for a finite dimensional approximation of a free boundary problem modeling solid fuel combustion c 2007 elsevier b v all rights reserved

borel moore homology riemann roch transformations and local terms abstract we develop various properties of etale borel moore homology and study its relationship with intersection theory using gabber s localized cycle classes we define etale homological gysin morphisms and show that they are compatible with the cycle class map and gysin morphisms in intersection theory we also study etale versions of bivariant operations and establish their compatibility with riemann roch transformations and fulton macpherson bivariant operations as an application of these techniques we show that in certain situations local terms for correspondences acting on etale cohomology are given by cycle classes

rigid geometry lefschetz verdier trace formula and deligne s conjecture in abstract algebraic geometry the lefschetz verdier trace formula expresses the global trace of an endomorphism induced on cohomology by a correspondence as a sum of local contributions called local terms near fixed points though the formula holds quite generally the explicit calculation of local terms is very hard to carry out and no good formula is known for general correspondences over the complex numbers a useful formula is known for a good class called weakly hyperbolic g m on the other hand in positive characteristics p deligne conjectured that the local terms would be much simplified if we composed a given correspondence with a high power of frobenius take a proper variety x over an algebraic closure k of a finite field fq a correspondence a y x xk x and a smooth qr k on an open set u of x fixed by a denote the inclusion by j and is invertible in k then

general fixed point formula for an algebraic surface and the theory of swan representations for two dimensional local rings 07755 1986 03 17 7755

local and global behavior near homoclinic orbits we study the local behavior of systems near homoclinic orbits to stationary points of saddle focus type we explicitly describe how a periodic orbit approaches homoclinicity and with the help of numerical examples discuss how these results relate to global patterns of bifurcations

the characteristic class and ramification of an l adic etale sheaf we introduce the characteristic class of an l adic etale sheaf using a cohomological pairing due to verdier sga5 as a consequence of the lefschetz verdier trace formula its trace computes the euler poincare characteristic of the sheaf we compare the characteristic class to two other invariants arising from ramification theory one is the swan class of kato saito 17 and the other is the 0 cycle class defined by kato for rank 1 sheaves in 16

jordan holder theorems for derived module categories of piecewise hereditary algebras abstract a jordan holder theorem is established for derived module categories of piecewise hereditary algebras in particular for representations of quivers and for hereditary abelian categories of a geometric nature the resulting composition series of derived categories are shown to be independent of the choice of bounded or unbounded derived module categories and also of the choice of finitely generated or arbitrary modules

structure des connexions meromorphes formelles de plusieurs variables et semi continuite de l irregularite we prove malgrange s conjecture on the absence of confluence phenomena for integrable meromorphic connections more precisely if y x is a complex analytic fibration by smooth curves z a hypersurface of y finite over x and an integrable meromorphic connection on y with poles along z then the function which attaches to x x the sum of the irregularities of the fiber x at the points of z x is lower semicontinuous

arithmetic and differential swan conductors of rank one representations with finite local monodromy we consider a complete discrete valuation field of characteristic p with possibly nonperfect residue field let rm v be a rank one continuous representation of its absolute galois group with finite local monodromy we will prove that the it arithmetic swan conductor of rm v defined after k kato which fits in the more general theory of abbes saito coincides with the it differential swan conductor of the associated differential module rm d dag rm v defined by k kedlaya this construction is a generalization to the nonperfect residue case of the fontaine s formalism as presented in the work of n tsuzuki our method of proof will allow us to give a new interpretation of the refined swan conductor

the characteristic cycle and the singular support of a constructible sheaf we define the characteristic cycle of an etale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by beilinson we prove a formula a la milnor for the total dimension of the space of vanishing cycles and an index formula computing the euler poincare characteristic generalizing the grothendieck ogg shafarevich formula to higher dimension an essential ingredient of the construction and the proof is a partial generalization to higher dimension of the semi continuity of the swan conductor due to deligne laumon we prove the index formula by establishing certain functorial properties of characteristic cycles

ramification theory for varieties over a perfect field for an l adic sheaf on a variety of arbitrary dimension over a perfect field we define the swan class measuring the wild ramification as a 0 cycle class supported on the ramification locus we prove a lefschetz trace formula for open varieties and a generalization of the grothendieck ogg shararevich formula using the swan class

infinitesimal deformation of p adic differential equations on berkovich curves we show that if a differential equation mathscr f over a quasi smooth berkovich curve x has a certain compatibility condition with respect to an automorphism sigma of x then mathscr f acquires a semi linear action of sigma i e lifting that on x the compatibility condition forces the automorphism sigma to be close to the identity of x so the above construction applies to a certain class of automorphisms called infinitesimal this generalizes andre and di vizio asterisque 1 296 55 111 2004 and pulita compos math 144 4 867 919 2008 we also obtain an application to morita s p adic gamma function and to related values of p adic l functions

the convergence newton polygon of a p adic differential equation i affinoid domains of the berkovich affine line we prove that the radii of convergence of the solutions of a p adic differential equation fancyscript f over an affinoid domain x of the berkovich affine line are continuous functions on x that factorize through the retraction of x to gamma of x onto a finite graph gamma subseteq x we also prove their super harmonicity properties this finiteness result means that the behavior of the radii as functions on x is controlled by a finite family of data

on rational fixed points of finite group actions on the affine space consider a finite l group acting on the affine space of dimension n over a field k whose characteristic differs from l we prove the existence of a fixed point rational over k in the following cases the field k is p special for some prime p different from its characteristic the field k is perfect and fertile and n 3

finite local monodromy of overconvergent unit root f isocrystals on a curve we prove that the category of p adic continuous representations of a fundamental group of a curve over a perfect field of a positive characteristic p with finite local monodromy is equivalent to that of overconvergent unit root f isocrystals on the curve to show the equivalence of categories we study the local theory and apply it to the global case

the structure and homological properties of generalized standard auslander reiten components abstract we describe the structure and homological properties of arbitrary generalized standard auslander reiten components of artin algebras in particular we prove that for all but finitely many indecomposable modules in such components the euler characteristic is defined and nonnegative further we provide a handy criterion for an infinite auslander reiten component of an artin algebra to be generalized standard we solve also the long standing open problem concerning the structure of artin algebras admitting a separating family of auslander reiten components