# An introduction to six-functor formalisms

@inproceedings{Gallauer2021AnIT, title={An introduction to six-functor formalisms}, author={Martin Gallauer}, year={2021} }

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 accompaniment for the beneﬁt of the audience. No originality is claimed.

## 4 Citations

### Six-functor formalism; why solid abelian groups?

- Mathematics
- 2022

These notes are based on a talk given the Intercity seminar of Winter 2022 on “Condensed Mathematics”, which follow [Schb]. The aim of the talk it to motivate the use of solid abelian groups in…

### Exponentiation of coefficient systems and exponential motives

- Mathematics
- 2022

We construct new six-functor formalisms capturing cohomological invariants of varieties with potentials. Starting from any six-functor formalism C, encoded as a coefficient system, we associate a new…

### The universal six-functor formalism

- MathematicsAnnals of K-Theory
- 2022

We prove that Morel-Voevodsky's stable $\mathbb{A}^1$-homotopy theory affords the universal six-functor formalism.

### Supports for constructible systems

- Mathematics
- 2021

We develop a ‘universal’ support theory for derived categories of constructible (ana-lytic or étale) sheaves, holonomic (cid:68) -modules, mixed Hodge modules and others. As applications we classify…

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