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An introduction to six-functor formalisms

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arxiv 2112.10456 v1 pith:VEDTUHER submitted 2021-12-20 math.AG math.KT

Martin Gallauer This is my paper · ORCID
classification math.AGmath.KT
keywords formalismintroductionnotessix-functoraccountalgebraicaudiencebenefit
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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.

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  1. Duality for KGL-modules in motivic homotopy theory

    math.KT 2025-07 unverdicted novelty 5.0 of 10

    Duality for KH-theory modules in motivic homotopy theory is proven over all quasi-excellent characteristic zero schemes, with G-theory as dualizing object.

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