Related papers: Modular representations of p-adic groups

We provide two examples of $\mathcal{D}$-modules in prime characteristic $p$ which answer two open problems in \cite{Lyubeznik} in the negative.

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

We show how a polar representation of a compact connected Lie group can be linearly determined from its dimension and isotropy subgroup data in the general reducible case.

For each prime $p$ and each positive integer $d$, we construct the first examples of second countable, topologically simple, $p$-adic Lie groups of dimension $d$ whose Lie algebras are abelian. This answers several questions of Gl\"ockner…

Let $pod_{\ell}(n)$ be the number of $\ell$-regular partitions of $n$ with distinct odd parts. In this article, prove that for any positive integer $k$, the set of non-negative integers $n$ for which $pod_{\ell}(n)\equiv 0 \pmod{p^{k}}$ has…

Let $G$ be a finite group, and let $\mathbf{K}_p$ denote the completion at $p$ of the complex $K$-theory spectrum. $\mathbf{K}_p$ is a commutative ring spectrum that in some ways is very similar to the usual ring $\mathbf{Z}_p$ of $p$-adic…

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…

We study the Modular Isomorphism Problem applying a combination of existing and new techniques. We make use of the small group algebra to give a positive answer for two classes of groups of nilpotency class 3. We also introduce a new…

We study the automorphism groups of the reduction $X_0(N) \times \bar{\mathbb{F}}_p$ of a modular curve $X_0(N)$ over primes $ p\nmid N$.

We prove the Identity Theorem for pro-$p$-groups with a single defining relation giving a positive feedback to a question of Serre on the structure of relation modules. A construction of "conjurings" indicates finality of our result in a…

Using the theory of $(\phi,\Gamma)$-modules and the formalism of Selmer complexes we construct the p-adic height for p-adic representations with coefficients in an affinoid algebra over $Q_p$.

Let $p$ be a prime number. We show in this short note that mod-$p$ maximal compact inductions of a $p$-adic split reductive group do not have irreducible admissible subrepresentations.

Let V be a p-adic representation of the absolute Galois group G of Q_p that becomes crystalline over a finite tame extension, and assume p odd. We provide necessary and sufficient conditions for V to be isomorphic to the Tate module V_p(A)…

Using methods of associative algebras, Lie theory, group cohomology, and modular representation theory, we construct profinite $p$-adic analytic groups such that the centralizer of each of their non-trivial elements is abelian. The paper…

We consider lifting of mod p representations to mod p^2 representations in the setting of representations of (i) finite groups; (ii) absolute Galois groups of abstract fields; and (iii) absolute Galois groups of local and global fields.

We introduce a geometric formalism for studying modular forms of half-integral weight and explore some of its basic properties. Geometric Hecke operators are constructed and some basic spaces of $p$-adic forms are introduced. The $p$-adic…

We develop a notion of cell decomposition suitable for studying weak p- adic structures (reducts of p-adic fields where addition and multiplication are not (everywhere) definable). As an example, we apply this to a language with restricted…

The number of maximal abelian subgroups of a finite p-group is shown to be congruent to 1 modulo p.

In this talk we discuss the relations between representations of algebraic groups and principal bundles on algebraic varieties, especially in characteristic $p$. We quickly review the notions of stable and semistable vector bundles and…

We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, and relate their geometry to the weight part of Serre's conjecture for GL(2).