Galois group, 222adeles, 149Artin’s conjecture, 293automorphic form, 292bar resolution, 172biquadratic reciprocity, 271Brauer group, 205Brauer-Hasse-Noether theorem, 252central simple algebra, 206centralizer, 206chain map, 163change of group, 184Chebotarev density theorem, 282class formation, 222class group, 33cohomological functor, 16...

Let p be a fixed prime number, V a group isomorphic to (Z/p) for some integer d and BV its classifying space. The exceptional properties of the mod p cohomology of BV , as an unstable module and algebra over the Steenrod algebra, have led to the calculation of the mod p cohomology of the mapping spaces with source BV as the image by a functor TV of the mod p cohomology of the target ([La2]). Th...

In this paper, we prove the conjectures made in a joint paper of the author with Carlson and Robinson, on the vanishing of cohomology of a nite group G. In particular, we prove that if k is a eld of characteristic p, then every non-projective kG-module M in the principal block has nontrivial cohomology in the sense that H (G;M) 6= 0, if and only if the centralizer in G of every element of order...

We construct a generalization of the usual module of indecomposables for the mod 2 cohomology of a finite //-space. Structure theorems are obtained regarding how the Steenrod algebra acts on this module.

A ghost in the stable module category of a group G is a map between representations of G that is invisible to Tate cohomology. We show that the only non-trivial finite p-groups whose stable module categories have no non-trivial ghosts are the cyclic groups C2 and C3. We compare this to the situation in the derived category of a commutative ring. We also determine for which groups G the second p...

The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

The equivariant Kazhdan-Lusztig polynomial of a braid matroid may be interpreted as the intersection cohomology of a certain partial compactification of the configuration space of n distinct labeled points in C, regarded as a graded representation of the symmetric group Sn. We show that, in fixed cohomological degree, this sequence of representations of symmetric groups naturally admits the str...

We prove that H( n 2)(SLn Z;Q) = 0, where ( n 2 ) is the cohomological dimension of SLn Z, and similarly for GLn Z. We also prove analogous vanishing theorems for cohomology with coefficients in a rational representation of the algebraic group GLn. These theorems are derived from a presentation of the Steinberg module for SLn Z whose generators are integral apartment classes, generalizing Manin...

We study the module category associated to the quantum double of a finite abelian group G twisted by a 3-cocycle, which is known to be a braided monoidal category, and investigate the question of when two such categories are equivalent. We base our discussion on an exact sequence which interweaves the ordinary and Eilenberg-Mac Lane cohomology of G. Roughly speaking, this reveals that the data ...

The purpose of this note is to establish a number of useful results about the augmentation ideal J for the coefficient ring F ∗ G of a Noetherian complex orientable equivariant cohomology theory. The results show that various naturally occurring substitutes for the ideal have the same radical, and can therefore be used instead of the augmentation ideal in all geometric constructions. 1. Stateme...