Related papers: General linear and functor cohomology over finite …

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We address the problem of computing in the group of $\ell^k$-torsion rational points of the jacobian variety of algebraic curves over finite fields, with a view toward computing modular representations.

For an arbitrary field p-torsion and cotorsion of the Milnor groups K_n(F) and K_n^{t}(F)=K_n(F)/\cap_{l\ge1} lK_n(F) are discussed. The work contains further discussions of an analogue of Satz 90 for K_n(F) and K_n^{t}(F) and computation…

We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We…

This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost…

In this short note we show that representation and character varieties of discrete groups can be viewed as tensor products of suitable functors over the PROP of cocommutative Hopf algebras. Such view point has several interesting…

We will use Watts's theorem together with Lenzing's characterization of finitely presented modules via commuting properties of the induced tensor functor in order to study commuting properties of Ext-covariant functors.

Let p be an odd prime. Let G be a p-local finite group over the extraspecial p-group p_+^{1+2}. In this paper we study the cohomology and the stable splitting of their p-complete classifying space BG.

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

We study the Picard groups of connected linear algebraic groups, and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every global function field. We also utilize our study of these…

For a prime number $p$, we give a new restriction on pro-$p$ groups $G$ which are realizable as the maximal pro-$p$ Galois group $G_F(p)$ for a field $F$ containing a root of unity of order $p$. This restriction arises from Kummer Theory…

We generalize a cohomological construction of representations due to Lusztig from the hyperspecial case to arbitrary parahoric subgroups of a reductive group over a local field, which splits over an unramified extension. We compute the…

We construct N-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ generalizing thereby the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge…

This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.

We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the…

As a part of our program for Geometric Arithmetic, we develop an arithmetic cohomology theory for number fields using theory of locally compact groups.

We give explicit, uniform formulas for the graded characters and total ranks of the Lie algebra homology of finite-dimensional representations in all classical types. In many cases, these compute the Tor groups of finite length modules over…

We determine the number of connected components of the moduli space for representations of a surface group in the general linear group.

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

We give a description of simple functors taking finitely generated values, from a small additive category to the category of vector spaces over a field. This result is analogous to Steinberg's tensor product theorems in group representation…