Comparison of Abelian categories recollements

We give a necessary and sufficient condition for a morphism between recollements of abelian categories to be an equivalence.Comment: 16 pages. To appear in Documenta Mathematic

Strict polynomial functors and coherent functors

We build an explicit link between coherent functors in the sense of Auslander and strict polynomial functors in the sense of Friedlander and Suslin. Applications to functor cohomology are discussed.Comment: published version, 24 pages. Section 2.7 reorganized, and notational distinction between left and right tensor product reinstalle

General linear and functor cohomology over finite fields

In recent years, there has been considerable success in computing Ext-groups of modular representations associated to the general linear group by relating this problem to one of computing Ext-groups in functor categories. In this paper, we extend our ability to make such Ext-group calculations by establishing several fundamental results. Throughout this paper, we work over fields of positive characteristic p.Comment: 66 pages, published version, abstract added in migratio

Power reductivity over an arbitrary base

Our starting point is Mumford's conjecture, on representations of Chevalley groups over fields, as it is phrased in the preface of "Geometric Invariant Theory". After extending the conjecture appropriately, we show that it holds over an arbitrary commutative base ring. We thus obtain the first fundamental theorem of invariant theory (often referred to as Hilbert's fourteenth problem) over an arbitrary Noetherian ring. We also prove results on the Grosshans graded deformation of an algebra in the same generality. We end with tentative finiteness results for rational cohomology over the integers.Comment: 24 p; Some finiteness results added for rational cohomology over the integer

LANNES' T FUNCTOR ON INJECTIVE UNSTABLE MODULES AND HARISH-CHANDRA RESTRICTION

In the 1980's, the magic properties of the cohomology of elementary abelian groups as modules over the Steenrod algebra initiated a long lasting interaction between topology and modular representation theory in natural characteristic. The Adams-Gunawardena-Miller theorem in particular, showed that their decomposition is governed by the modular representations of the semi-groups of square matrices. Applying Lannes' T functor on the summands L P := Hom Mn(Fp) (P, H * (F p) n) defines an intriguing construction in representation theory. We show that T(L P) ∼ = L P ⊕ H * V 1 ⊗ L δ(P) , defining a functor δ from F p [M n (F p)]-projectives to F p [M n−1 (F p)]-projectives. We relate this new functor δ to classical constructions in the representation theory of the general linear groups

Spaces with Noetherian cohomology

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? In this paper we provide, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-grou

Spaces with Noetherian cohomology

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements, with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group

Spaces with Noetherian cohomology

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements, with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.Comment: 12 page