Axiomatic characterization of ordinary differential cohomology

Axiomatic Characterization of Ordinary Differential Cohomology

Ĥ satisfies the Character Diagram shown in §1 and thus has natural transformations onto both closed differential forms with integral periods and integral cohomology. It was shown in [6] that an enriched version of the Weil homomorphism, carrying both an invariant polynomial and an associated integral homology class of the classifying space, naturally factors through Ĥ on its way to these target...

Ordinary and Generalized Sheaf Cohomology

This article is expanded from a talk given by the author in (the preliminary version of) the Student Algebraic Topology seminar in University of Michigan, Ann Arbor. The rst part will be a review of ordinary sheaf cohomology which is done in such a way that generalization to generalized sheaf cohomology theory becomes automatic. The second part is a quick introduction of the approach to general...

Tate Cohomology in Axiomatic Stable Homotopy Theory

Group Cohomology of the Universal Ordinary Distribution

Abstract. For any odd squarefree integer r, we get complete description of the Gr = Gal(Q(μr)/Q) group cohomology of the universal ordinary distribution Ur in this paper. Moreover, if M is a fixed integer which divides l−1 for all prime factors l of r, we study the cohomology group H(Gr, Ur/MUr). In particular, we explain the mysterious construction of the elements κr′ for r |r in Rubin[10], wh...

Chromatic Characteristic Classes in Ordinary Group Cohomology

We study a family of subrings, indexed by the natural numbers, of the mod p cohomology of a finite group G. These subrings are based on a family of vn-periodic complex oriented cohomology theories and are constructed as rings of generalised characteristic classes. We identify the varieties associated to these subrings in terms of colimits over categories of elementary abelian subgroups of G, na...