Vol. 11, No. 8, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 10, 1681–1865
Issue 9, 1533–1680
Issue 8, 1359–1532
Issue 7, 1239–1357
Issue 6, 1127–1237
Issue 5, 981–1126
Issue 4, 805–980
Issue 3, 541–804
Issue 2, 267–539
Issue 1, 1–266

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Quasi-Galois theory in symmetric monoidal categories

Bregje Pauwels

Vol. 11 (2017), No. 8, 1891–1920
Abstract

Given a ring object A in a symmetric monoidal category, we investigate what it means for the extension A to be (quasi-)Galois. In particular, we define splitting ring extensions and examine how they occur. Specializing to tensor-triangulated categories, we study how extension-of-scalars along a quasi-Galois ring object affects the Balmer spectrum. We define what it means for a separable ring to have constant degree, which is a necessary and sufficient condition for the existence of a quasi-Galois closure. Finally, we illustrate the above for separable rings occurring in modular representation theory.

Keywords
tensor triangulated category, separable, etale, Galois, ring-object, stable category
Mathematical Subject Classification 2010
Primary: 18BXX
Secondary: 16GXX, 18GXX
Milestones
Received: 1 September 2016
Revised: 29 May 2017
Accepted: 9 July 2017
Published: 15 October 2017
Authors
Bregje Pauwels
Mathematical Sciences Institute
The Australian National University
Acton ACT 2601
Australia