A tour of support theory for triangulated categories through Tensor triangular geometry

Stevenson, G. (2018) A tour of support theory for triangulated categories through Tensor triangular geometry. In: Herbera, D., Pitsch, W. and Zarzuela, S. (eds.) Building Bridges Between Algebra and Topology. Series: Advanced courses in mathematics - CRM Barcelona. Birkhäuser: Cham, Switzerland, pp. 63-101. ISBN 9783319701561 (doi: 10.1007/978-3-319-70157-8_2)

Abstract

These notes give a short survey of the approach to support theory and the study of lattices of triangulated subcategories through the machinery of tensor triangular geometry. One main aim is to introduce the material necessary to state and prove the local-to-global principle. In particular, we discuss Balmer’s construction of the spectrum, generalised Rickard idempotents and support for compactly generated triangulated categories, and actions of tensor triangulated categories. Several examples are also given along the way. These notes are based on a series of lectures given during the Spring 2015 program on ‘Interactions between Representation Theory, Algebraic Topology and Commutative Algebra’ (IRTATCA) at the Centre de Recerca Matemàtica CRM-Barcelona.

• Item Type: Book Sections
• Status: Published
• Glasgow Author(s) Enlighten ID: Stevenson, Dr Gregory
• Authors: Stevenson, G.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Publisher: Birkhäuser
• ISBN: 9783319701561
• Published Online: 01 April 2018
• Copyright Holders: Copyright © 2018 Springer International Publishing AG, part of Springer Nature
• First Published: First published in Building Bridges Between Algebra and Topology: 63-101
• Publisher Policy: Reproduced in accordance with the publisher copyright policy