Analytic Tate spaces and reciprocity laws
type: Item
instance of: scholarly article
zbMATH Open document ID: 1320.30003
author: Ricardo García López
publication date: 2014-11-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1211.4722
Mathematics Subject Classification ID: 30B10
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 14H99
zbMATH DE Number: 6365883
zbMATH Keywords: Laurent series
zbMATH Keywords: nuclear Fréchet spaces
zbMATH Keywords: strong dual of nuclear Fréchet spaces
MaRDI profile type: Publication
OpenAlex ID: W2963403657
arXiv ID: 1211.4722
DOI: 10.1093/IMRN/RNT105
published in: IMRN. International Mathematics Research Notices
title: Analytic Tate spaces and reciprocity laws
review text: The author introduces an analytic version of the notion of Tate spaces. An \textit{analytic Tate space} is defined as a topological vector space splitting as the direct sum of a nuclear Fréchet space and the strong dual of a nuclear Fréchet space. The ring of Laurent power series \(k((t))\) is an example of a Tate space which is also an analytic Tate space. Others examples are given, including \(\mathcal{O}_{\hat{0}}\), the ring of germs of analytic functions on a punctured neighborhood of \(0\in \mathbb{C}\).NEWLINENEWLINEThe aim of the paper is to show that some results valid for Tate spaces do extend to the new analytic situation. The author defines commutator symbols, and proves reciprocity laws for algebraic curves, in the complex and \(p\)-adic analytic cases.
reviewed by: Laurent Battisti
description: scientific article; zbMATH DE number 6365883