Related papers: Block decompositions for $p$-adic classical groups…

For any torsion-free hyperbolic group $\Gamma$ and any group $G$ that is fully residually $\Gamma$, we construct algorithmically a finite collection of homomorphisms from $G$ to groups obtained from $\Gamma$ by extensions of centralizers,…

For the group of endo-permutation modules of a finite \(p\)-group, there is a surjective reduction modulo \(p\) homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic \(p\). We prove…

This series of papers is a contribution to the program of classifying $p$-blocks of finite groups up to source algebra equivalence, starting with the case of cyclic blocks. To any $p$-block $\mathbf{B}$ of a finite group with cyclic defect…

In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the…

If G is a finite group and p is a prime number, we investigate the relationship between the p-modular decomposition numbers of characters of height zero in the principal p-block of G and the p-local structure of G.

Suppose that $G$ is the group of $F$-points of a connected reductive group over $F$, where $F/\mathbb{Q}_p$ is a finite extension. We study the (topological) irreducibility of principal series of $G$ on $p$-adic Banach spaces. For unitary…

The power classes of a field are well-known for their ability to parameterize elementary $p$-abelian Galois extensions. These classical objects have recently been reexamined through the lens of their Galois module structure. Module…

We give, in Sections 2 and 3, an english translation of: {\it Classes g\'en\'eralis\'ees invariantes}, J. Math. Soc. Japan, 46, 3 (1994), with some improvements and with notations and definitions in accordance with our book: {\it Class…

The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…

Let p be an odd prime. We show that the classification of p-divisible groups by Breuil windows and the classification of finite flat group schemes of p-power order by Breuil modules hold over any complete regular local ring with perfect…

An explicit understanding of the (category of all smooth, complex) representations of p-adic groups provides an important tool not just within representation theory. It also has applications to number theory and other areas, and, in…

Let $k$ be an algebraically closed field of characteristic $p>0$ and $G$ a finite group. We provide a description of the torsion subgroup $TT(G)$ of the finitely generated abelian group $T(G)$ of endo-trivial $kG$-modules when $p=2$ and $G$…

The formal deformation space of a supersingular Barsotti-Tate group over of dimension two equipped with an action of Z_{p^2} is known to be isomorphic to the formal spectrum of a power series ring in two variables. If one chooses an extra…

Let $T$ be a complete, model-complete, geometric dp-minimal $\mathcal{L}$-theory of topological fields of characteristic $0$ and let $T(\partial)$ be the theory of expansions of models of $T$ by a derivation $\partial$. We assume that…

Let $G$ be a group, $F$ a field, and $A$ a finite-dimensional central simple algebra over $F$ on which $G$ acts by $F$-algebra automorphisms. We study the ideals and subalgebras of $A$ which are preserved by the group action. Let $V$ be the…

Let $\mathcal{R}$ be the Grothendieck ring of complex smooth finite-length representations of the sequence of p-adic groups $\{GL_n(F)\}_{n=0}^\infty$, with multiplication defined through parabolic induction. We study the problem of the…

Let $G$ be a p-adic classical group (orthogonal, symplectic, unitary) and $\pi$ be an epipelagic representation of $G$ defined by Reeder-Yu. Using M{\oe}glin's theory of extended cuspidal supports and Bushnell-Kutzko's theory of covering…

We provide some experimental results on the decomposition of the parabolic induction of $\pi\otimes\pi$ in the Grothendieck group where $\pi$ is an irreducible representation of $GL_n$ over a local non-archimedean field.

We investigate generalizations along the lines of the Mordell--Lang conjecture of the author's $p$-adic formal Manin--Mumford results for $n$-dimensional $p$-divisible formal groups $\mathcal{F}$. In particular, given a finitely generated…

We first provide a detailed proof of Kato's classification theorem of log $p$-divisible groups over a noetherian henselian local ring. Exploring Kato's idea further, we then define the notion of a standard extension of a classical finite…