Related papers: A refinement of the Artin conductor and the base c…

Let F be a nonarchimedean local field and let G = GL(n) = GL(n,F). Let E/F be a finite Galois extension. We investigate base change E/F at two levels: at the level of algebraic varieties, and at the level of K-theory. We put special…

Let K be a local field of mixed characteristic not absolutely ramified. Fontaine-Laffaille theory gives a description of the torsion crystalline Z_p-representations of the absolute Galois group of K (p denotes the characteristic of the…

We explain how to reconstruct the category of Artin-Tate $\mathbb{R}$-motivic spectra as a deformation of the purely topological $C_2$-equivariant stable category. The special fiber of this deformation is algebraic, and equivalent to an…

The present paper is a continuation of earlier work by Gunnar Carlsson and the first author on a motivic variant of the classical Becker-Gottlieb transfer and an additivity theorem for such a transfer by the present authors. Here, we…

Let k be a number field and K/k Galois. We transform the construction of the unramified Brauer group of the norm one torus R^1_K/k(G_m) into the construction of a special abelian extension over K. If k=Q and K/Q biquadratic, we explicitly…

Let K be a finite extension of Q_p with residue field F_q and let P(T) = T^d + a_{d-1}T^{d-1} + ... +a_1 T, where d is a power of q and a_i is in the maximal ideal of K for all i. Let u_0 be a uniformizer of O_K and let {u_n}_{n \geq 0} be…

Let K and F be complete discrete valuation fields of residue characteristic p>0. Let m be a positive integer no more than their absolute ramification indices. Let s and t be their uniformizers. Let L/K and E/F be finite extensions such that…

We prove the existence of a new structure on the first Galois cohomology of generic families of symplectic self-dual $p$-adic representations of $G_{\mathbb{Q}_p}$ of rank two (a local sign decomposition): a functorial decomposition into…

Let S/R be a finite extension of discrete valuation rings of characteristic p>0, and suppose that the corresponding extension L/K of fields of fractions is separable and is H-Galois for some K-Hopf algebra H. Let D_{S/R} be the different of…

Let K be a complete discretely valued field of mixed characteristic (0, p) with possibly imperfect residue field. We prove a Hasse-Arf theorem for the arithmetic ramification filtrations on G_K, except possibly in the absolutely unramified…

An extension $K/k$ of analytic (i.e. real valued complete) fields is called small if it is topologically-algebraically generated by finitely many elements. We prove that this property is inherited by subextensions and hence topological…

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is…

To any solution of a linear system of differential equations, we associate a kernel, correlators satisfying a set of loop equations, and in presence of isomonodromic parameters, a Tau function. We then study their semiclassical expansion…

We adapt a technique of Kisin to construct and study crystalline deformation rings of $G_K$ for a finite extension $K/\mathbb{Q}_p$. This is done by considering a moduli space of Breuil--Kisin modules, satisfying an additional Galois…

Clausen has constructed a homotopical enrichment of the Artin reciprocity symbol in class field theory. On the Galois side, Selmer K-homology replaces the abelianized Galois group, while on the automorphic side the K-theory of locally…

In this paper we prove that the complement to the affine complex arrangement of type \widetilde{B}_n is a K(\pi, 1) space. We also compute the cohomology of the affine Artin group G of type \widetilde{B}_n with coefficients over several…

Let A be a comodule algebra for a finite dimensional Hopf algebra K over an algebraically closed field k, and let A^K be the subalgebra of invariants. Let Z be a central subalgebra in A, which is a domain with quotient field Q. Assume that…

Let $p>2$ be a prime. Let $K$ be a tamely ramified finite extension over $\mathbb Q_p$ with ramification index $e$, and let $G_K$ be the Galois group. We study Kisin modules attached to crystalline representations of $G_K$ whose labeled…

Our goal is to give a purely algebraic characterization of finite abelian Galois covers of a complete, irreducible, non-singular curve $X$ over an algebraically closed field $\k$. To achieve this, we make use of the Galois theory of…

The difference between the Faltings height of an abelian variety $A$ defined over a number field $k$ and its stable height is measured by the so-called base change conductor. In this paper, we give a uniform bound of the base change…