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An introduction to six-functor formalisms

Martin Gallauer

Vol. 6 (2025), 63–106
Abstract

These are notes for a mini-course given at the summer school and conference The six-functor formalism and motivic homotopy theory in Milan 9/2021. They provide an introduction to the formalism of Grothendieck’s six operations in algebraic geometry and end with an excursion to rigid-analytic motives.

The notes do not correspond precisely to the lectures delivered but provide a more self-contained account for the benefit of the audience and others. No originality is claimed.

Keywords
six operations, six-functor formalism, motivic homotopy theory, cohomology, rigid-analytic motives
Mathematical Subject Classification
Primary: 14F08, 14F99
Milestones
Received: 20 December 2021
Revised: 28 December 2022
Accepted: 28 December 2022
Published: 15 March 2025
Authors
Martin Gallauer
Mathematics Institute
University of Warwick
Coventry
United Kingdom