Local-global Galois theory of arithmetic function fields

Autor:	Harbater, David, Hartmann, Julia, Krashen, Daniel, Parimala, R., Suresh, V.
Rok vydání:	2017
Předmět:	Mathematics - Rings and Algebras Mathematics - Algebraic Geometry Mathematics - Number Theory 12F10 13F25 14H25 (primary) 13B05 14H05 20E18 (secondary)
Druh dokumentu:	Working Paper
Popis:	We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for local separable extensions to descend to global extensions, and for the local absolute Galois group to inject into the global absolute Galois group. As an application we obtain a local-global principle for the index of a variety over such a function field. In this context we also study algebraic versions of van Kampen's theorem, describing the global absolute Galois group as a pushout of local absolute Galois groups. Comment: 26 pages. Some reorganization of Section 3.2, with a new remark; notation in Section 3.3 for absolute Galois groupoids has been modified and made more consistent; slightly expanded introduction
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1710.03635 Zobrazit plný text záznamu View this record from Arxiv