Langlands correspondence and constructive Galois theory. Abstracts from the workshop held February 2--8, 2014.
type: Item
instance of: scholarly article
title: Langlands correspondence and constructive Galois theory. Abstracts from the workshop held February 2--8, 2014.
zbMATH Open document ID: 1349.00140
DOI: 10.4171/OWR/2014/05
published in: Oberwolfach Reports
publication date: 2016-11-30T00:00:00Z
review text: Summary: Recent progress in the Langlands programm provides a significant step towards the understanding of the arithmetic of global fields. The geometric Langlands program provides a systematic way to construct \(\ell\)-adic sheaves (resp. \(\mathcal D\)-modules) on algebraic curves which subsumes the construction of classical sheaves, like rigid local systems, used in inverse Galois theory (by Belyi, Malle, Matzat, Thompson, Dettweiler, Reiter) for the construction of field extension of the rational function fields \(\mathbb F_p(t)\) or \(\mathbb Q(t)\) (recent work of Heinloth, Ngo, Yun and Yun). On the other hand, using Langlands correspondence for the field \(\mathbb Q\), Khare, Larsen and Savin constructed many new automorphic representations which lead to new Galois realizations for classical and exceptional groups over \(\mathbb Q\). It was the aim of the workshop, to bring together the experts working in the fields of Langlands correspondence and constructive Galois theory.
Mathematics Subject Classification ID: 00B05
Mathematics Subject Classification ID: 00B25
Mathematics Subject Classification ID: 14-06
Mathematics Subject Classification ID: 14D24
Mathematics Subject Classification ID: 11S37
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 12F12
zbMATH DE Number: 6657987
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/owr/2014/05
OpenAlex ID: W2014655591
description: scientific article; zbMATH DE number 6657987