Related papers: Serre conjecture II for pseudo-reductive groups

We give a reduction of Donovan's conjecture for abelian groups to a similar statement for quasisimple groups. Consequently we show that Donovan's conjecture holds for abelian $2$-groups.

In this paper we determine the precise extent to which the classical sl_2-theory of complex semisimple finite-dimensional Lie algebras due to Jacobson--Morozov and Kostant can be extended to positive characteristic. This builds on work of…

We prove that the group $\mathrm{SAut}_{\mathrm{k}}(\mathbb{A}^2)$ is simple as an algebraic group of infinite dimension, over any infinite field $\mathrm{k}$, by proving that any closed normal subgroup is either trivial or the whole group.…

We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on rank two unitary groups for odd primes l. We propose a conjectural set of Serre weights,…

The classification of elliptic curves E over the rationals Q is studied according to their torsion subgroups E_{tors}(Q) of rational points. Explicit criteria for the classification are given when E_{tors}(Q) are cyclic groups with even…

It was conjectured by Gorsky, Hogancamp, Mellit, and Nakagane that the left and right adjoints of the parabolic induction functor between homotopy categories of Soergel bimodules associated to a finite Coxeter group are related by the…

A conjecture of Huneke and Wiegand claims that, over one-dimensional commutative Noetherian local domains, the tensor product of a finitely generated, non-free, torsion-free module with its algebraic dual always has torsion. Building on a…

We show that the Simple Loop Conjecture holds for any representation $\rho\colon\pi_1(S)\longrightarrow \text{PSL}(2,\,\mathbb R)$ that is discrete but not faithful. That is, we show the existence of a simple closed curve in the kernel of…

The Bogomolov Conjecture is a finiteness statement about algebraic points of small height on a smooth complete curve defined over a global field. We verify an effective form of the Bogomolov Conjecture for all curves of genus at most 4…

Cais, Ellenberg and Zureick-Brown recently observed that over finite fields of characteristic two, all sufficiently general smooth plane projective curves of a given odd degree admit a non-trivial rational 2-torsion point on their Jacobian.…

A semisimple algebraic tensor category over an algebraically closed field k of characteristic zero is the representation category of all finite dimensional twisted super representations of an affine reductive supergroup G over k. Such a…

Watkins's conjecture suggests that for an elliptic curve $E/\mathbb{Q}$, the rank of the group $E(\mathbb{Q})$ of rational points is bounded above by $\nu_2 (m_E)$, where $m_E$ is the modular degree associated with $E$. It is known that…

To a tree of semi-simple algebras we associate a qurve (or formally smooth algebra) S. We introduce a Zariski- and etale quiver describing the finite dimensional representations of S. In particular, we show that all quotient varieties of…

We prove the refined Loughran--Smeets conjecture of Loughran--Rome--Sofos for a wide class of varieties arising as products of conic bundles. One interesting feature of our varieties is that the subordinate Brauer group may be arbitrarily…

We prove the Morrison-Kawamata cone conjecture for klt Calabi-Yau pairs in dimension 2. That is, for a large class of rational surfaces as well as K3 surfaces and abelian surfaces, the action of the automorphism group of the surface on the…

We extend the decomposition conjecture to 2d quantum field theories with a gauged $\text{Rep}(H)$ symmetry category for $H$ a finite-dimensional semisimple Hopf algebra with $\text{Rep}(G)$ trivially-acting and $\text{Vec}(\Gamma)$ the…

We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection…

We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive $p$-adic group. The method of proof is to establish the presence of a very simple geometric…

The purpose of this short note is to study Serre functors of categories of quasicoherent sheaves on stacks of the form $\mathcal{Y} = \mathrm{Spec} A/G$ where $G$ is a reductive group acting on $\mathrm{Spec} A$ with a unique closed orbit.…

Torsors under affine groups are generalized in the super context by super-torsors under affine super-groups. We investigate those super-torsors by using Hopf-algebra language and techniques. It is explicitly shown, under suitable…