Related papers: Productive elements in group cohomology

We propose a new method for studying $n$- and $\Gamma$-cohomology of globalizations of Harish-Chandra modules, where $G=KAN$ is a rank one semisimple Lie group, $\Gamma$ is a discrete subgroup of $G$ and $n=Lie(N)$. We prove a conjecture of…

We consider formal power series $f(z) = \omega z + a_2z^2 + \ldots \ (\omega \neq 0)$, with coefficients in a field of characteristic $0$. These form a group under the operation of composition (= substitution). We prove (Theorem 1) that…

Given a commutative ring $A$, a "formal $A$-module" is a formal group equipped with an action of $A$. There exists a classifying ring $L^A$ of formal $A$-modules. This paper proves structural results about $L^A$ and about the moduli stack…

In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…

We show that, if $M$ is a subspace lattice with the property that the rank one subspace of its operator algebra is weak* dense, $L$ is a commutative subspace lattice and $P$ is the lattice of all projections on a separable infinite…

We construct the cohomology groups with compact support of stacks of shtukas with $\mathbb Z_{\ell}$-coefficients. We construct the cuspidal cohomology groups and prove that they are $\mathbb Z_{\ell}$-modules of finite type. We prove that…

A path factor in a graph $G$ is a factor of $G$ in which every component is a path on at least two vertices. Let $T\Box P_n$ be the Cartesian product of a tree $T$ and a path on $n$ vertices. Kao and Weng proved that $T\Box P_n$ is…

Answering a long-standing question in the theory of torsion modules, we show that weakly productively bounded domains are necessarily productively bounded. Moreover, we prove a twin result for the ideal lattice L of a domain equating weak…

This paper investigates the effective categoricity of ultrahomogeneous structures. It is shown that any computable ultrahomogeneous structure is $\Delta^0_2$ categorical. A structure A is said to be weakly ultrahomogeneous if there is a…

The positive cohomology groups of a finite group acting on a ring vanish when the ring has a norm-one element. In this note we give explicit homotopies on the level of cochains when the group is cyclic, which allows us to express any…

Let $G$ be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic $p$. Let $I$ be a pro-$p$ Iwahori subgroup of $G$ and let $R$ be a commutative quasi-Frobenius ring. If…

Let $G$ be an abelian group of order $n$ and let $R$ be a commutative ring which admits a homomorphism ${\Bbb Z}[\zeta_{n}]\ra R$, where $\zeta_{n}$ is a (complex) primitive $n$-th root of unity. Given a finite $R[G\e]$-module $M$, we…

Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group…

Let H be a separable, infinite dimensional Hilbert space and let S be a countable subset of H. Then most positive operators on H have the property that every nonzero vector in the span of S is cyclic, in the sense that the set of operators…

Let $t$ be a positive integer. Following work of D. M. Davis, we study the topology of complex-projective product spaces, i.e. quotients of cartesian products of odd dimensional spheres by the diagonal $S^1$-action, and of the $t$-torsion…

Let $R$ be an affine algebra over an algebraically closed field of characteristic $0$ with dim$(R)=n$. Let $P$ be a projective $A=R[T_1,\cdots,T_k]$-module of rank $n$ with determinant $L$. Suppose $I$ is an ideal of $A$ of height $n$ such…

We show that in a weak globular $\omega$-category, all composition operations are equivalent and commutative for cells with sufficiently degenerate boundary, which can be considered a higher-dimensional generalisation of the Eckmann-Hilton…

Let $A$ be a differential graded algebra with cohomology ring $H^*A$. A graded module over $H^*A$ is called \emph{realisable} if it is (up to direct summands) of the form $H^*M$ for some differential graded $A$-module $M$. Benson, Krause…

Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial.…

Let ${\mathscr G}$ be a linear algebraic group over $k$, where $k$ is an algebraically closed field, a pseudo-finite field or the valuation ring of a nonarchimedean local field. Let $G= {\mathscr G}(k)$. We prove that if $\gamma, \delta\in…