Related papers: Finiteness of \'etale fundamental groups by reduct…

We give a proof of the finite generation of the cohomology ring of a finite p-group over F_p by reduction to the case of elementary abelian groups, based on Serre's Theorem on products of Bocksteins.

In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…

This is an introduction to the finite groups, with focus on the groups of permutations and reflections, and more generally, on the finite groups of unitary matrices. We first discuss the basics of group theory, featuring the cyclic,…

We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.

Motivated by recent results on the minimal base of a permutation group, we introduce a new local invariant attached to arbitrary finite groups. More precisely, a subset Delta of a finite group G is called a p-base (where p is a prime) if…

We examine which representations of the absolute Galois group of a field of finite characteristic with image over a finite field of the same characteristic may be constructed by the Galois group's action on the division points of an…

We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…

We develop a package using the computer algebra system GAP for computing the decomposition of a representation $\rho$ of a finite group $G$ over $\mathbb{C}$ into irreducibles, as well as the corresponding decomposition of the centraliser…

We study cohomologies of a curve with an action of a finite $p$-group over a field of characteristic $p$. Assuming the existence of a certain 'magical element' in the function field of the curve, we compute the equivariant structure of the…

We prove the finiteness of leaps of modules of $m$-integrable derivations for algebras essentially of finite type and, more generally, for schemes essentially of finite type over an algebraically closed field of positive characteristic.…

The concept of descent algebras over a field of characteristic zero is extended to define descent algebras over a field of prime characteristic. Some basic algebraic structure of the latter, including its radical and irreducible modules, is…

I will survey some results in the theory of modular representations of a reductive $p$-adic group, in positive characteristic $\ell \neq p$ and $\ell=p$.

Given a field $k$ of characteristic zero and an indeterminate $T$ over $k$, we investigate the local behaviour at primes of $k$ of finite Galois extensions of $k$ arising as specializations of finite Galois extensions $E/k(T)$ (with $E/k$…

We introduce a general constructive method to find a p-basis (and the Ulm invariants) of a finite Abelian p-group M. This algorithm is based on Groebner bases theory. We apply this method to determine the additive structure of…

We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…

A criterion for the HNN-extension of a finite p-group to be residually a finite p-group is obtained and based on this criterion the sufficient condition for residuality a finite p-group of HNN-extension with arbitrary base group is proved.…

This survey is about old and new results about the modular representation theory of finite reductive groups with a strong emphasis on local methods. This includes subpairs, Brauer's Main Theorems, fusion, Rickard equivalences. In the…

Voevodsky proved that normal schemes of finite type over finitely generated fields of characteristic $0$ can be reconstructed from their \'etale sites. Let $K$ be a field that is finitely generated over $\mathbb{F}_p(t)$. Grothendieck…

Many open conjectures in the representation theory of finite groups can be studied by reducing them to related questions about quasi-simple groups. In such studies, $p$-radical subgroups typically play a critical role. To classify the…

We study cohomology for $p$-local finite groups with non-constant coefficient systems. In particular we show that under certain restrictions there exists a cohomology transfer map in this context, and deduce the standard consequences.