Signatures of Witt spaces with boundary

The L-class of Non-witt Spaces

Corrigendum to “Intersection homology with field coefficients: K-Witt spaces and K-Witt bordism”

This note corrects an error in the char(K) = 2 case of the author’s computation of the bordism groups of K-Witt spaces for the field K. A complete computation is provided for the unoriented bordism group. For the oriented bordism groups, a nearly complete computation is provided as well a discussion of the difficulty of resolving a remaining ambiguity in dimensions equivalent to 2 mod 4. Recall...

Witt groups of sheaves on topological spaces

This paper investigates the Witt groups of triangulated categories of sheaves (of modules over a ring R in which 2 is invertible) equipped with Poincare-Verdier duality. We consider two main cases, that of perfect complexes of sheaves on locally compact Hausdorff spaces and that of cohomologically constructible complexes of sheaves on polyhedra. We show that the Witt groups of the latter form a...

Intersection homology with field coefficients: K-Witt spaces and K-Witt bordism

We construct geometric examples of pseudomanifolds that satisfy the Witt condition for intersection homology Poincaré duality with respect to certain fields but not others. We also compute the bordism theory of K-Witt spaces for an arbitrary field K, extending results of Siegel for K = Q. 2000 Mathematics Subject Classification: 55N33, 57Q20, 57N80

The Basic Geometry of Witt Vectors, Ii Spaces

This is an account of the algebraic geometry of Witt vectors and arithmetic jet spaces. The usual, “p-typical” Witt vectors of p-adic schemes of finite type are already reasonably well understood. The main point here is to generalize this theory in two ways. We allow not just p-typical Witt vectors but those taken with respect to any set of primes in any ring of integers in any global field, fo...