The six operations in equivariant motivic homotopy theory

By Marc Hoyois. 2015

160 citations recorded by the source corpus.

Abstract We introduce and study the homotopy theory of motivic spaces and spectra parametrized by quotient stacks [ X / G ] , where G is a linearly reductive linear algebraic group. We extend to this equivariant setting the main foundational results of motivic homotopy theory: the (unstable) purity and gluing theorems of Morel–Voevodsky and the (stable) ambidexterity theorem of Ayoub. Our proof of the latter is different than Ayoub's and is of interest even when G is trivial. Using these results, we construct a formalism of six operations for equivariant motivic spectra, and we deduce that any cohomology theory for G -schemes that is represented by an absolute motivic spectrum satisfies descent for the cdh topology.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/41382ea1332ef0c96d7ae3b1bce61d61fb207d18

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In Geometry and Topology

1. M. Levine
2. Markus Spitzweck
3. O. Rondigs
4. Vladimir Voevodsky
5. Thomas H. Geisser
6. P. Ostvaer
7. Frédéric Déglise
8. P. Østvær

In Mathematical Physics

1. M. Levine
2. Markus Spitzweck
3. O. Rondigs
4. P. Ostvaer
5. Thomas H. Geisser
6. Frédéric Déglise
7. P. Østvær
8. Ivan Panin

Citations in the corpus

• Aspects of Enumerative Geometry with Quadratic Forms (2017, background): “erting the characteristic whenever working in the non-perfect case. 1.1. Duality for smooth projective varieties. We begin by recalling the construction of Σ∞ TX ∨ + by Hoyois, Hu, Riou and Voevodsky [18, 19, 30, 37]; our discussion follows [37, §2]. We first take the case X = Pd k, which we denote b”