Related papers: P-adic Nori Theory

We find upper and lower bounds of the multiplicities of irreducible admissible representations $\pi$ of a semisimple Lie group $G$ occurring in the induced representations $Ind_H^G\tau$ from irreducible representations $\tau$ of a closed…

A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant…

The p-adic description of Higgs mechanism in TGD framework provides excellent predictions for elementary particle and hadrons masses ([email protected] 9410058-62). The gauge group of TGD is just the gauge group of the standard model so…

In this paper we describe some properties of groups $G$ that contain a solvable subgroup of finite prime-power index (Theorem 1 and Corollaries 2--3). We prove that if $G$ is a non-solvable group that contains a solvable subgroup of index…

A profinite group is index-stable if any two isomorphic open subgroups have the same index. Let $p$ be a prime, and let $G$ be a compact $p$-adic analytic group with associated $\mathbb{Q}_p$-Lie algebra $\mathcal{L}(G)$. We prove that $G$…

Let $G$ be a commutative algebraic group defined over a number field $K$ that is disjoint over $K$ to $\mathbb G_a$ and satisfies the condition of semistability. Consider a linear form $l$ on the Lie algebra of $G$ with algebraic…

Let G be a reductive group over an algebraically closed field of positive characteristic. In this article we show an analogue for Morozov theorem for characteristics that are separably good for G (and under additional hypotheses on the…

Let $X$ be a variety (possibly non-complete or singular) over a finitely generated field $k$ of characteristic $0$. For a prime number $\ell$, let $\rho_\ell$ be the Galois representation on the first $\ell$-adic cohomology of $X$. We show…

Fix a positive integer $g$ and rational prime $p$. We prove the existence of a genus $g$ curve $C/\mathbb{Q}$ such that the mod $p$ representation of its Jacobian is tame by imposing conditions on the endomorphism ring. As an application,…

We discuss the following conjecture of Kitaoka: if a finite subgroup $G$ of $GL_{n}(O_{K})$ is invariant under the action of $Gal(K/\Bbb Q)$ then it is contained in $GL_{n}(K^{ab})$. Here $O_{K}$ is the ring of integers in a finite, Galois…

We describe a general method for giving $p$-adic interpretations of $G$-functions arising from degenerating periods of smooth projective algebraic varieties. Using this, we are able to implement a strategy due to Andr\'e for bounding…

Motivated by the Farrell-Jones Conjecture for group rings, we formulate the $\mathcal{C}$op-Farrell-Jones Conjecture for the K-theory of Hecke algebras of td-groups. We prove this conjecture for (closed subgroups of) reductive p-adic groups…

We study G-valued semi-stable Galois deformation rings where G is a reductive group. We develop a theory of Kisin modules with G-structure and use this to identify the connected components of crystalline deformation rings of minuscule…

It is shown that in the units of augmentation one of an integral group ring $\mathbb{Z} G$ of a finite group $G$, a noncyclic subgroup of order $p^{2}$, for some odd prime $p$, exists only if such a subgroup exists in $G$. The corresponding…

Let $\pi$ be a proper subset of the set of all primes. Denote by $r$ the smallest prime which does not belong to $\pi$ and set $m = r$ if $r = 2$ or $3$ and $m = r-1$ if $r \geqslant 5$. We study the following conjecture: a conjugacy class…

This note presents some equalities in law for $Z_N:=\det(\Id-G)$, where $G$ is an element of a subgroup of the set of unitary matrices of size $N$, endowed with its unique probability Haar measure. Indeed, under some general conditions,…

Let $R$ be a commutative Noetherian ring of prime characteristic $p$. The main goal of this paper is to study in some detail when \[ \overline{W^R}:=\{\mathfrak{p}\in\operatorname{Spec} (R):\ \mathcal{F}^{E_{\mathfrak{p}}}\text{ is finitely…

In this article, we establish results concerning the cohomology of Zariski dense subgroups of solvable linear algebraic groups. We show that for an irreducible solvable $\mathbb{Q}$-defined linear algebraic group $\mathbf{G}$, there exists…

It is well known that the Tchebotarev density theorem implies that an irreducible $\ell$-adic representation $\rho$ of the absolute Galois group of a number field $K$ is determined (up to isomorphism) by the characteristic polynomials of…

Let $f : X \to S$ be a smooth projective family defined over $\mathcal{O}_{K}[\mathcal{S}^{-1}]$, where $K \subset \mathbb{C}$ is a number field and $\mathcal{S}$ is a finite set of primes. For each prime $\mathfrak{p} \in…