the u invariant of the function fields of p adic curves the u invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field it is an open question whether the u invariant of function fields of p aidc curves is 8 in this paper we answer this question in the affirmative for function fields of nondyadic p adic curves

hermitian k theory of the integers rognes and weibel used voevodsky s work on the milnor conjecture to deduce the strong dwyer friedlander form of the lichtenbaum quillen conjecture at the prime 2 in consequence the 2 completion of the classifying space for algebraic k theory of the integers z 1 2 can be expressed as a fiber product of well understood spaces bo and bgl f3 over bu similar results are now obtained for hermitian k theory and the classifying spaces of the integral symplectic and orthogonal groups for the integers z 1 2 this leads to computations of the 2 primary hermitian k groups and affirmation of the lichtenbaum quillen conjecture in the framework of hermitian k theory

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

motivic cohomology over dedekind rings we study properties of bloch s higher chow groups on smooth varieties over dedekind rings we prove the vanishing of open image in new window for i n and the existence of a gersten resolution for open image in new window if the residue characteristic is p we also show that the bloch kato conjecture implies the beilinson lichtenbaum conjecture open image in new window an identification open image in new window for m invertible and a gersten resolution with arbitrary finite coefficients over a complete discrete valuation ring of mixed characteristic 0 p we construct a map from motivic cohomology to syntomic cohomology which is a quasi isomorphism provided the bloch kato conjecture holds

a generalization of serre s condition mathrm f f with applications to the finiteness of unramified cohomology in this paper we introduce a condition mathrm f m on a field k for a positive integer m that generalizes serre s condition f and which still implies the finiteness of the galois cohomology of finite galois modules annihilated by m and algebraic k tori that split over an extension of degree dividing m as well as certain groups of etale and unramified cohomology various examples of fields satisfying mathrm f m including those that do not satisfy f are given

triangular witt groups part ii from usual to derived we establish that the derived witt group is isomorphic to the usual witt group when 2 is invertible this key result opens the ali baba s cave of triangular witt groups linking the abstract results of part i to classical questions for the usual witt group for commercial purposes we survey the future applications of triangular witt groups in the introduction we also establish a connection between odd indexed witt groups and formations finally we prove that over a commutative local ring in which 2 is a unit the shifted derived witt groups are all zero but the usual one

accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1d center bundle we prove that stable ergodicity is cr open and dense among conservative partially hyperbolic diffeomorphisms with one dimensional center bundle for all r 2

on the bernoulli property for certain partially hyperbolic diffeomorphisms abstract we address the classical problem of equivalence between kolmogorov and bernoulli property of smooth dynamical systems in a natural class of volume preserving partially hyperbolic diffeomorphisms homotopic to anosov derived from anosov on 3 torus we prove that kolmogorov and bernoulli properties are equivalent in our approach we propose to study the conditional measures of volume along central foliation to recover fine ergodic properties for partially hyperbolic diffeomorphisms as an important consequence we obtain that there exists an almost everywhere conjugacy between any volume preserving derived from anosov diffeomorphism of 3 torus and its linearization our results also hold in higher dimensional case when central bundle is one dimensional and stable and unstable foliations are quasi isometric

the mayer vietoris principle for grothendieck witt groups of schemes we prove localization and zariski mayer vietoris for higher gro thendieck witt groups alias hermitian k groups of schemes admitting an ample family of line bundles no assumption on the characteristic is needed and our schemes can be singular along the way we prove additivity fibration and approximation theorems for the hermitian k theory of exact categories with weak equivalences and duality

cohomological invariants for quadratic forms over local rings let a be local ring in which 2 is invertible and let n be a non negative integer we show that the nth cohomological invariant of quadratic forms is a well defined homomorphism from the nth power of the fundamental ideal in the witt ring of a to the degree n etale cohomology of a with mod 2 coefficients which is surjective and has kernel the hbox n 1 th power of the fundamental ideal this is obtained by proving the gersten conjecture for witt groups in an important mixed characteristic case

duality via cycle complexes we show that bloch s complex of relative zero cycles can be used as a dualizing complex over perfect fields and number rings this leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields finite fields local fields of mixed characteristic and rings of integers in number rings generalizing results which so far have only been known for smooth schemes or in low dimensions and unifying the p adic and l adic theory as an application we generalize rojtman s theorem to normal projective schemes

fuzzy systems and controllers lyapunov tools for a regionwise approach this paper reviews a class of tools which can help to check the stability of fuzzy linguistic controllers which is a difficult task due to their regionwise structure the application of conventional methods when considering a fuzzy controller as a global nonlinear controller often leads to conservative stability results the use of appropriate continuous or piecewise continuous lyapunov functions allows to address the stability of nonlinear systems under fuzzy control while taking into account the local structure of the fuzzy controllers some methods are presented which enforce the global lyapunov function to decrease when leaving one subspace for another closer to the equilibrium using concentric domains and providing less conservative conditions

on brauer groups of double covers of ruled surfaces let x be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2 the main result of this paper is a finite presentation of the 2 torsion in the brauer group of x with generators given by central simple algebras over the function field of x and relations coming from the neron severi group of x in particular the result gives a central simple algebra representative for the unique nontrivial brauer class on any enriques surface an example demonstrating the applications to the study of rational points is given

some remarks on the stability of mamdani fuzzy control systems this paper presents a passivity approach to the stability analysis of mamdani fuzzy control systems the main idea of the paper is that the fuzzy controller can be considered from an input output viewpoint as a nonlinear dissipative operator an input output approach is provided by considering a dynamical dependency of inputs of the fuzzy controller then the passivity theory is applied in order to obtain conditions for absolute stability of the closed loop control system

finiteness theorems for the shifted witt and higher grothendieck witt groups of arithmetic schemes abstract for smooth varieties over finite fields we prove that the shifted aka derived witt groups of surfaces are finite and the higher grothendieck witt groups aka hermitian k theory of curves are finitely generated for more general arithmetic schemes we give conditional results for example finite generation of the motivic cohomology groups implies finite generation of the grothendieck witt groups

levels of function fields of surfaces over number fields we study the level of nonformally real function fields of surfaces over number fields and show that it is at most 4 for a large class of surfaces

comments on practical design of nonlinear fuzzy controllers with stability analysis for regulating processes with unknown mathematical models it is shown in this note that the fuzzy controller with locally linear control rules used in ying 1994 cannot be linearized around the origin and therefore local stability of closed loop systems including this type of fuzzy controller cannot be analyzed by means of the lyapunov s first method besides it is proved that with another choice of inference law the fuzzy controller with locally linear control rules can be linearized in a neighbourhood of the origin copyright c 1996 elsevier science ltd

etale duality for constructible sheaves on arithmetic schemes in this note we relate the following three topics for arithmetic schemes a general duality for etale constructible torsion sheaves a theory of etale homology and the arithmetic complexes of gersten bloch ogus type defined by k kato kct in brief there is an absolute duality using certain dualizing sheaves on these schemes we describe and characterize the dualizing sheaves to some extent relate them to symbol maps define etale homology via the dualizing sheaves and show that the niveau spectral sequence for the latter constructed by the method of bloch and ogus bo leads to the complexes defined by kato some of these relations may have been expected by experts and some have been used implicitly in the literature although we do not know any explicit reference for statements or proofs moreover the main results are used in a crucial way in a paper by two of us js so a major aim is to fill a gap in the literature and a special emphasis is on precise formulations including the determination of signs but the general picture developed here may be of interest itself

period index and u invariant questions for function fields over complete discretely valued fields let k be a complete discretely valued field with residue field and f the function field of a curve over k let p be the characteristic of and l a prime not equal to p if the brauer l dimensions of all finite extensions of are bounded by d and the brauer l dimensions of all extensions of of transcendence degree at most 1 are bounded by d 1 then it is known that the brauer l dimension of f is at most d 2 lieblich in j reine angew math 659 1 41 2011 saltman in j ramanujan math soc 12 25 47 1997 harbater et al in invent math 178 231 263 2009 in this paper we give a bound for the brauer p dimension of f in terms of the p rank of as an application we show that if is a perfect field of characteristic 2 then any quadratic form over f in at least 9 variables is isotropic this leads to the fact that every element in h 3 f mathbb z 2 mathbb z is a symbol if is a finite field of characteristic 2 u f 8 is a result of heath brown leep heath brown in compos math 146 271 287 2010 leep in j reine angew math 2013 to appear

chow witt groups and grothendieck witt groups of regular schemes let a be a noetherian commutative z 1 2 algebra of krull dimension d and let p be a projective a module of rank d we use derived grothendieck witt groups and euler classes to detect some obstructions for p to split off a free factor of rank one if d 3 we show that the vanishing of its euler class in the corresponding grothendieck witt group is a necessary and sufficient condition for p to have a free factor of rank one if d is odd we also get some results in that direction if a is regular we show that the chow witt groups defined by morel and barge appear naturally as some homology groups of a gersten type complex in grothendieck witt theory from this we deduce that if d 3 then the vanishing of the euler class of p in the corresponding chow witt group is a necessary and sufficient condition for p to have a free factor of rank one crown copyright c 2008 published by elsevier inc all rights reserved