The six operations in equivariant motivic homotopy theory

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• 作者：Marc Hoyois¹ ; ^{hoyois@mit.edu" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：14F42 ; 55P91
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：10 January 2017
• 年：2017
• 卷：305
• 期：Complete
• 页码：197-279
• 全文大小：1106 K

文摘

We introduce and study the homotopy theory of motivic spaces and spectra parametrized by quotient stacks [X/G]$[X/G]$, 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.