Related papers: Contraction par Frobenius de G-modules

Let k be a field of characteristic p>0. A theorem of de Jong shows that morphisms of modules over W(k)[[t]] with Frobenius and connection structure descend from the completion of W(k)((t)). A careful reading of de Jong's proof suggests the…

We study the decomposition of tensor products between a Steinberg module and a costandard module, both as a module for the algebraic group $G$ and when restricted to either a Frobenius kernel $G_r$ or a finite Chevalley group…

For any finite-dimensional factorizable ribbon Hopf algebra H and any ribbon automorphism omega of H, we establish the existence of the following structure: an H-bimodule F_omega and a bimodule morphism Z_omega from Lyubashenko's Hopf…

Let $N$ be a normal subgroup of a group $G$. An $N$-module $Q$ is $G$-stable provided that $Q$ is equivalent to the twist $Q^g$ of $Q$ by $g$, for every $g\in G$. If the action of $N$ on $Q$ extends to an action of $G$ on $Q$, $Q$ is…

Let $G$ be a simply connected and simple algebraic group defined and split over a finite prime field $\mathbb{F}_p$ of $p$ elements. In this paper, using an $\mathbb{F}_p$-linear map splitting Frobenius endomorphism on a hyperalgebra…

Gendo-Frobenius algebras are a common generalisation of Frobenius algebras and of gendo-symmetric algebras. A comultiplication is constructed for gendo-Frobenius algebras, which specialises to the known comultiplications on Frobenius and on…

Let R be a regular ring essentially of finite type over a perfect field k. An R-module M is called a unit R[F]-module if it comes equipped with an isomorphism F*M-->M where F denotes the Frobenius map on Spec R, and F* is the associated…

In this paper, given a semisimple algebraic group $\bf G$ of rank 2, we construct a special semiorthogonal decomposition in the derived category of coherent sheaves on the flag variety ${\bf G}/{\bf B}$. These decompositions are defined…

Let G be a totally disconnected, locally compact group admitting a contractive automorphism f. We prove a Jordan-Holder theorem for series of f-stable closed subgroups of G, classify all possible composition factors and deduce consequences…

We prove the semisimplicity conjecture for A-motives over finitely generated fields K. This conjecture states that the rational Tate modules V_p(M) of a semisimple A-motive M are semisimple as representations of the absolute Galois group of…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

Let A be a supersingular abelian variety over a finite field k. We give an approximate description of the structure of the group A(k) of rational points of A over k in terms of the characteristic polynomial f of the Frobenius endomorphism…

We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…

For a split quasireductive supergroup $G$ defined over a field, we study structure and representation of Frobenius kernels $G_r$ of $G$ and we give a necessary and sufficient condition for $G_r$ to be unimodular in terms of the root system…

We study Lie algebroids in positive characteristic and moduli spaces of their modules. In particular, we show a Langton's type theorem for the corresponding moduli spaces. We relate Langton's construction to Simpson's construction of…

Let L be a preprojective algebra of Dynkin type, and let G be the corresponding complex semisimple simply connected algebraic group. We study rigid modules in subcategories sub(Q) for Q an injective L-module, and we introduce a mutation…

Assume $G$ is a connected reductive algebraic group defined over $\bar{\mathbb{F}_p}$ such that $p$ is good prime for $G$. Furthermore we assume that $Z(G)$ is connected and $G/Z(G)$ is simple of classical type. Let $F$ be a Frobenius…

Let $G$ be a simple algebraic group defined over a finite field of good characteristic, with associated Frobenius endomorphism $F$. In this article we extend an observation of Lusztig, (which gives a numerical relationship between an…

Let $k$ be a nonperfect field of characteristic $2$. Let $G$ be a $k$-split simple algebraic group of type $E_6$ (or $G_2$) defined over $k$. In this paper, we present the first examples of nonabelian non-$G$-completely reducible…

Recently, E.Feigin introduced a very interesting contraction $\mathfrak q$ of a semisimple Lie algebra $\mathfrak g$ (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic…