Related papers: Kato's conductor and generic residual perfection

Kato's inequality is shown for the magnetic relativistic Schr\"odinger operator $H_{A,m}$ defined as the operator theoretical {\it square root} of the selfadjoint, magnetic nonrelativistic Schr\"odinger operator $(-i\nabla-A(x))^2+m^2$ with…

Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to…

We introduce and study a special class of Kato manifolds, which we call toric Kato manifolds. Their construction stems from toric geometry, as their universal covers are open subsets of toric algebraic varieties of non-finite type. This…

Let $p$ be a prime number, $n$ an integer $\geq 2$, and $L$ a finite extension of $\mathrm{Q}_p$. Let $\rho_L$ be an $n$-dimensional (non-critical but not necessary generic) potentially crystalline $p$-adic Galois representation of the…

We prove that the non-ordinary component is connected in the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This was conjectured by Kisin. As an application to global Galois…

A two-dimensional Galois representation into the Hecke algebra of Katz modular forms of weight one over a finite field of characteristic p is constructed and is shown to be unramified at p in most cases.

This paper contains a complete proof of Fukaya's and Kato's epsilon$-isomorphism conjecture in [23] for invertible \Lambda-modules (the case of V = V_0(r) where V_0 is unramified of dimension 1). Our results rely heavily on Kato's…

Let $\mathcal O$ be the ring of integers in a finite extension of $\mathbb Q_p$. If $G$ is a finite group and $\Gamma$ is a maximal order containing the group ring $\mathcal O[G]$, Jacobinski's conductor formula gives a complete description…

We prove a variety of results on the existence of automorphic Galois representations lifting a residual automorphic Galois representation. We prove a result on the structure of deformation rings of local Galois representations, and deduce…

The present notes are the expanded and polished version of three lectures given in Stanford, concerning the analytic and arithmetic properties of weight one modular forms. The author tried to write them in a style accessible to…

We prove Chai's conjecture on the additivity of the base change conductor of semiabelian varieties in the case of Jacobians of proper curves. This includes the first infinite family of non-trivial wildly ramified examples. Along the way, we…

Let K be a complete discrete valuation field of mixed characteristic (0,p) and G_K the absolute Galois group of K. In this paper, we will prove the p-adic monodromy theorem for p-adic representations of G_K without any assumption on the…

In this paper, a strong multiplicity one theorem for Katz modular forms is studied. We show that a cuspidal Katz eigenform which admits an irreducible Galois representation is in the level and weight old space of a uniquely associated Katz…

The Galilean conformal algebra has recently been realised in the study of the non-relativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field…

In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product $\mathbb{R}\times N^{n-1}$, or globally conformally equivalent to the Euclidean space $\mathbb{R}^{n}$…

Let V be a crystalline p-adic representation of the absolute Galois group G_K of an finite unramified extension K of Q_p and T a lattice of V stable by G_K. We prove the following result: Let Fil^1 V be the maximal sub-representation of V…

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations…

Let $K$ be a totally real number field of degree $r$. Let $K_{\infty}$ denote the cyclotomic $\mathbb{Z}_{2}$-extension of $K$ and let $L_{\infty}$ be a finite extension of $K_{\infty}$, abelian over $K$. The goal of this paper is to…

We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal automorphic representations of $\GL_2(\A_F)$, $F$ a totally real…

We give a complete classification of all the potentially crystalline 3-adic representations of the absolute Galois group of $\mathbb{Q}_3$ that are isomorphic to the Tate module of an elliptic curve defined over $\mathbb{Q}_3$. These…