Related papers: The p-adic local monodromy theorem for fake annuli

We consider the semiring of abstract finite dynamical systems up to isomorphism, with the operations of alternative and synchronous execution. We continue searching for efficient algorithms for solving polynomial equations of the form $P(X)…

We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call `potential diagonalizability'. This result allows for `change of weight' and seems to be substantially more flexible…

We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform…

We give a new class of multidimensional $p$-adic continued fraction algorithms. We propose an algorithm in the class for which we can expect that multidimensional $p$-adic version of Lagrange's Theorem holds.

In this paper, we prove a new continuous embedding theorem for fractional Sobolev spaces with variable exponents into variable exponent Lebesgue spaces on unbounded domains. As an application, we study a class of nonlocal elliptic problems…

This paper gives an elementary proof of an improved version of the algebraic Local B\'ezout Theorem (given by the authors in JSC 45 (2010) 975--985). Here we remove some ad hoc hypotheses and obtain an optimal algebraic version of the…

We formulate an equivariant version of Greenberg's $p$-adic Artin conjecture for smoothed equivariant $p$-adic Artin $L$-functions in the context of an arbitrary one-dimensional admissible $p$-adic Lie extension of a totally real number…

Similarly to the global case, the local structure of a holomorphic subvariety at a given point is described by its local irreducible decomposition. Following the paradigm of numerical algebraic geometry, an algebraic subvariety at a point…

We compute the $p$-adic densities of points with a given splitting type along a (generically) finite map, analogous to the classical Chebotarev theorem over number fields and function fields. Under some mild hypotheses, we prove that these…

Let $F$ be a CM number field. We generalize existing automorphy lifting theorems for regular residually irreducible $p$-adic Galois representations over $F$ by relaxing the big image assumption on the residual representation.

We present new techniques for removing arrows of bound quiver algebras, reducing thus the Finitistic Dimension Conjecture $\mathsf{(FDC)}$ for a given algebra to a smaller one. Unlike the classic arrow removal operation of…

We wish to draw attention to an interesting and promising interaction of two theories. On the one hand, it is the theory of \textbf{pseudo-triangulations} which was useful for implicit solution of thecarpenter's rule problem and proved…

In this paper, we give a complete real-variable theory of local variable Hardy spaces. First, we present various real-variable characterizations in terms of several local maximal functions. Next, the new atomic and the finite atomic…

Let $M$ be a multiplicative monoid with identity. Then I show that there is a universal one dimensional formal group law equipped with an action of $M$. If $M$ is $p$-perfect (i.e. $m\mapsto m^p$ is an isomorphism for some prime number $p$)…

Inspired by Emerton's work for GL(2), we study the completed cohomology of the tower of finite sets associated with a definite unitary group in two variables. When p splits (and other technical assumptions are fulfilled), we show that the…

We prove $p$-adic versions of a classical result in arithmetic geometry stating that an irreducible subvariety of an abelian variety with dense torsion has to be the translate of a subgroup by a torsion point. We do so in the context of…

We prove that over totally real fields, the $p$-adic Galois representations attached to non-self-dual regular algebraic cuspidal automorphic representations of $\mathrm{GL}(4)$ are irreducible. We then develop the theory of extra-twists in…

In this paper we generalize work of Amice and Lazard from the early (nineteen) sixties. Amice determined the dual of the space of locally Qp-analytic functions on Zp and showed that it is isomorphic to the ring of rigid functions on the…

In this paper, we extend the investigation of four-dimensional partially alternative algebras $\mathcal A$ initiated in \cite{HNT}. The partial alternativity condition, a natural generalization of the alternativity axiom, broadens the class…

We start with background that goes into an Iwahori-theoretic reformulation of the mod $p$ Local Langlands Correspondence (\S 2). We then explain some classical $p$-adic functional analytic results (\S 3) that go into defining the $p$-adic…