Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

$τ$-tilting theory: a self-contained introduction

Arne Johannsmann

Abstract

A self-contained introduction to the basics of Tau-tilting theory. We assume that the reader is familiar with Auslander-Reiten theory, but circumvent the need for the Brenner-Butler tilting theorem completely.

$τ$-tilting theory: a self-contained introduction

Abstract

A self-contained introduction to the basics of Tau-tilting theory. We assume that the reader is familiar with Auslander-Reiten theory, but circumvent the need for the Brenner-Butler tilting theorem completely.
Paper Structure (17 sections, 53 theorems, 66 equations)

This paper contains 17 sections, 53 theorems, 66 equations.

Table of Contents

  1. Introduction
  2. Notation and Preliminaries
  3. Torsion Theories
  4. Torsion Theories
  5. Covers and Envelopes
  6. Tau-rigid Modules
  7. Tau-rigid Modules
  8. On the Number of Summands
  9. The Upper Bound
  10. Tilting Modules
  11. Tau-tilting modules
  12. Support Rank
  13. Tau-tilting Modules
  14. Bijections
  15. Bongartz Completion
  16. ...and 2 more sections

Key Result

Theorem 1

Given $A$-modules $X, Y$, we obtain the following isomorphisms:

Theorems & Definitions (139)

  • Definition 1
  • Definition 2
  • Theorem : Auslander-Reiten Formula
  • Proposition 3
  • proof
  • Definition 1.1
  • Remark 1.2
  • Proposition 1.3
  • proof
  • Example 1.4
  • ...and 129 more