Witt groups of function fields of hyperelliptic curves

The local cohomology modules H^J _I(M) of a Matlis reflexive module are shown to be I-cofinite when j >= 1 and have finite Bass numbers when j >= 0, where I is an ideal satisfying any one of a list of properties. In addition, we show that the completion of a Matlis reflexive module is finitely generated over the completion of the ring and we classify Matlis reflexive modules over a one dimensional ring.     

Generalized Witt groups

In this paper we construct a functor from the category of one-dimensional commutative formal groups to the category of topological Abelian groups. For a multiplicative formal group, this function is the usual Witt functor. We study certain properties of the constructed functor. This functor is then used to describe multiplicative operations in the theory of unitary cobordisms.Translated from Matematicheskie Zametki, Vol. 13, No. 3, pp. 419–426, March, 1973.     

Witt groups and unipotent elements in algebraic groups

Let G be a semisimple algebraic group defined over an algebraicallyclosed field K of good characteristic p>0. Let u be a unipotentelement of G of order p^t, for some t N. In this paper it isshown that u lies in a closed subgroup of G isomorphic to theit Witt group W^t(K), which is a t-dimensional connected abelianunipotent algebraic group. 2000 Mathematics Subject Classification:20G15.     

On coherent hermitian Witt groups

We prove homotopy invariance for coherent hermitian Witt groups of Azumaya algebras with involutions over separated Gorenstein schemes of finite Krull dimension. We also generalize the zero theorem for the transfer and show that the Gersten conjecture holds for the hermitian Gersten–Witt complex of flat coherent algebras over a regular local ring which contains a field.     

Homotopy invariance of coherent Witt groups

 We prove the following general homotopy invariance theorem for coherent Witt groups: Let be a flat morphism of separated Gorenstein schemes of finite Krull dimension with affine fibers,i.e. π⁻¹(y) is an affine space over the residue field k(y) for all yY, then the induced homomorphism of coherent Witt groups is an isomorphism. As an application we calculate the (classical) Witt group of the affine hyperbolic sphere over a regular local ring. Received: 22 August 2001; in final form: 22 June 2002 / Published online: 1 April 2003     

Shifted Witt groups of semi-local rings

We show that the odd-indexed derived Witt groups of a semi-local ring with trivial involution vanish. We show that this is wrong when the involution is not trivial and we provide examples.The first author was supported by the Swiss National Science Foundation, grant 620-66065. The second author would like to thank the ETH-Zurich for its generous support.     

Witt groups and the elementary type conjecture

Let A be an algebra with involution * over a field F of characteristic zero and Id(A, *) the ideal of the free algebra with involution of *-identities of A. By means of the representation theory of the hyperoctahedral group Z ₂wrS _n we give a characterization of Id(A, *) in case the sequence of its *-codimensions is polynomially bounded. We also exhibit an algebra G ₂ with the following distinguished property: the sequence of *-codimensions of Id(G ₂, *) is not polynomially bounded but the *-codimensions of any T-ideal U properly containing Id(G ₂, *) are polynomially bounded.