Related papers: Fesenko reciprocity map

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…

The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations…

We consider the class of complete discretely valued fields such that the residue field is of prime characteristic p and the cardinality of a $p$-base is 1. This class includes two-dimensional local and local-global fields. A new definition…

For a finite totally ramified extension $L$ of a complete discrete valuation field $K$ with the perfect residue field of characteristic $p>0$, it is known that $L/K$ is an abelian extension if the upper ramification breaks are integers and…

We present a sharpened version of the Cohen-Gabber theorem for equicharacteristic, complete local domains (A,m,k) with algebraically closed residue field and dimension d > 0. Namely, we show that for any prime number p, Spec(A) admits a…

One extends P. Deligne's notion of integrality over a finite field for a $\ell$-adic sheaf on a scheme of finite type over a local field with finite residue field. One shows that this integrality notion is preserved by $Rf_!$, as it is over…

A local analogue of the Grothendieck Conjecture is an equivalence of the category of complete discrete valuation fields $K$ with finite residue fields of characteristic $p\ne 0$ and the category of absolute Galois groups of fields $K$…

We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and the totally ramified value number for a wider class of…

We prove a version of the Gindikin-Karpelevich formula for untwisted affine Kac-Moody groups over a local field of positive characteristic. The proof is geometric and it is based on the results of [1] about intersection cohomology of…

We define a class of pre-ordered abelian groups that we call finite-by-Presburger groups, and prove that their theory is model-complete. We show that certain quotients of the multiplicative group of a local field of characteristic zero are…

Akbarov's theory of holomorphic reflexivity for topological Hopf algebras has been developed in two directions, namely, by the complication of definitions when expanding the scope and by their simplification when restricting. In the…

As a continuation of arXiv:1412.6888, we study the reciprocity map for an open curve $X$ over a local field of characteristic $p>0$. We determine the $p$-part of the kernel of the reciprocity map after restricting ramification when the rank…

In this expository article, we outline a basic theory of group (co)homology and prove a cohomological formulation of the Local Reciprocity Law: $${\rm Gal}(L/K)^{\rm ab} \cong H_T^{-2}({\rm Gal}(L/K),\mathbb{Z}) \cong H_T^{0}({\rm…

We prove an assortment of results on (commutative and unital) NIP rings, especially $\mathbb{F}_p$-algebras. Let $R$ be a NIP ring. Then every prime ideal or radical ideal of $R$ is externally definable, and every localization $S^{-1}R$ is…

We reinterpret Kim's non-abelian reciprocity maps for algebraic varieties as obstruction towers of mapping spaces of etale homotopy types, removing technical hypotheses such as global basepoints and cohomological constraints. We then extend…

Let E/F be a quadratic extension of p-adic fields. The local Langlands correspondence establishes a bijection between n-dimensional Frobenius semisimple representations of the Weil-Deligne group of E and smooth, irreducible representations…

We revisit the local metaplectic correspondence previously constructed and studied by Flicker and Kazhdan. After restoring and generalizing some of their results, we get several interesting applications to the representation theory of a…

In this paper we introduce the local Nori fundamental group scheme of a reduced scheme or algebraic stack over a perfect field $k$. We give particular attention to the case of fields: to any field extension $K/k$ we attach a pro-local group…

We generalize the reciprocity theorem of G.R.~Robinson, D. Benson and P. Webb between a finite group and its subgroup to the case of finite-dimensional {\it symmetric} algebras over a field which are connected by a bimodule for the two…

We consider four classes of classical groups over a non-archimedean local field F: symplectic, (special) orthogonal, general (s)pin and unitary. These groups need not be quasi-split over F. The main goal of the paper is to obtain a local…