Related papers: Lubin's conjecture for height-one $p$-adic dynamic…

The geometry of the Lubin-Tate space of deformations of a formal group is studied via an \'etale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of…

We consider finite-dimensional Hopf algebras $u$ which admit a smooth deformation $U\to u$ by a Noetherian Hopf algebra $U$ of finite global dimension. Examples of such Hopf algebras include small quantum groups over the complex numbers,…

We build a one-variable $p$-adic $L$-function attached to two Hida families of ordinary $p$-stabilised newforms $\mathbf{f}$, $\mathbf{g}$, interpolating the algebraic part of the central values of the complex $L$-series $L(f \otimes…

In this paper we study the longstanding conjecture of whether there exists a noninner automorphism of order $p$ for a finite non-abelian $p$-group. We prove that if $G$ is a finite non-abelian $p$-group such that $G/Z(G)$ is powerful then…

We prove the weight part of Serre's conjecture in generic situations for forms of $U(3)$ which are compact at infinity and split at places dividing $p$ as conjectured by Herzig. We also prove automorphy lifting theorems in dimension three.…

With the Poincar\'e group $\mathbf{R}^{3,\,1}\rtimes O(3,\,1)$ as the model of departure, we focus, for $n=p+q$, $p+q\ge 4$, on the affine indefinite orthogonal group $\mathbf{R}^{p,q}\rtimes SO(p,\,q)$. Denote by $\mathfrak{h}_{p,\,q}$ the…

We prove a conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups $G$ defined over an algebraically closed field $\mathbb{k}$ of characteristic $0$. That is, if $\Phi\colon G\longrightarrow G$…

We initiate the study of p-adic algebraic groups G from the stability-theoretic and definable topological-dynamical points of view, that is, we consider invariants of the action of G on its space of types over Q_p in the language of fields.…

This article studies the finite--slope analogue of Loeffler's conjectural framework for Rankin--Selberg $p$-adic $L$-functions in universal deformation families. Starting from residual representations $\bar\rho_1,\bar\rho_2$ of tame…

For $K$ an imaginary quadratic field with discriminant $-D_K$ and associated quadratic Galois character $\chi_K$, Kojima, Gritsenko and Krieg studied a Hermitian Maass lift of elliptic modular cusp forms of level $D_K$ and nebentypus…

The main objective of this article is to establish the $p$-adic Artin formalism for the algebraic $p$-adic $L$-functions attached to the adjoint representations of Coleman families of modular forms. In particular, we prove a factorization…

We parameterize the finite-dimensional irreducible representations of a class of pointed Hopf algebras over an algebraically closed field of characteristic zero by dominant characters. The Hopf algebras we are considering arise in the work…

We compute the $p$-central and exponent-$p$ series of all right angled Artin groups, and compute the dimensions of their subquotients. We also describe their associated Lie algebras, and relate them to the cohomology ring of the group as…

Andrews and Petsche proposed in 2020 a conjectural characterization of all pairs $(f,\alpha)$, where $f$ is a polynomial over a number field $K$ and $\alpha\in K$, such that the dynamical Galois group of the pair $(f,\alpha)$ is abelian. In…

We study certain formal group laws equipped with an action of the cyclic group of order a power of $2$. We construct $C_{2^n}$-equivariant Real oriented models of Lubin-Tate spectra $E_h$ at heights $h=2^{n-1}m$ and give explicit formulas…

Let $p$ be a prime number and let $K$ be a genus one two-bridge knot. In the spirit of arithmetic topology, we observe that if $p$ divides the size of the 1st homology group of some odd-th cyclic branched cover of the knot $K$, then its…

Kirillov's orbit theory provides a powerful tool for the investigation of irreducible unitary representations of many classes of Lie groups. In a previous paper we used a modification hereof, called monomial linearisation, to construct a…

We study the action on the deformation space of a formal group by the maximal finite subgroup $G$ of its automorphisms, at the first height where the group has nontrivial $p$-torsion for odd $p$. We show given this group $G$ there is a…

Let G be a finite group of Lie type, defined over a field k of characteristic p > 0. We find explicit bounds for the dimension of the first cohomology group for G with coefficients in a simple kG-module. We proceed by bounding the number of…

Let $ F$ be an imaginary quadratic field and $\mathcal{O}$ its ring of integers. Let $ \mathfrak{n} \subset \mathcal{O} $ be a non-zero ideal and let $ p> 5$ be a rational inert prime in $F$ and coprime with $\mathfrak{n}$. Let $ V$ be an…