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A Tour of Support Theory for Triangulated Categories Through Tensor Triangular Geometry

  • Greg Stevenson
Chapter
Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

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.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Greg Stevenson
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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