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Chirantan Chowdhury | Motivic homotopy theory of algebraic stacks

EIMI, PDMI RAS and Chebyshev Laboratory
822 subscribers
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447 views 3 years ago
Seminar on A1-topology, motives and K-theory, March 11, 2022 Chirantan Chowdhury (University of Duisburg-Essen) Motivic homotopy theory of algebraic stacks In this talk, we extend the stable motivic homotopy theory from schemes to a large class of algebraic stacks using the language of ∞-categories. This includes quasi-separated algebraic spaces, local quotient stacks (for example moduli of vector bundles). We also extend the six functor formalism and prove statements like localization and purity. We start the talk by motivating the need of such specific class of algebraic stacks which shall lead up to the construction of the stable homotopy functor and the four functors f^*, f_*, −⊗− and Hom(−,−). Then we briefly explain the construction of the exceptional functors, base change and projection formula using the so called ”Enhanced Operation Map” due to Liu and Zheng. The talk ends by stating the other properties of these six functors like localization and purity. ...more
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Chirantan Chowdhury | Motivic homotopy theory of algebraic stacks
6Likes
447Views
2022Mar 11
Seminar on A1-topology, motives and K-theory, March 11, 2022 Chirantan Chowdhury (University of Duisburg-Essen) Motivic homotopy theory of algebraic stacks In this talk, we extend the stable motivic homotopy theory from schemes to a large class of algebraic stacks using the language of ∞-categories. This includes quasi-separated algebraic spaces, local quotient stacks (for example moduli of vector bundles). We also extend the six functor formalism and prove statements like localization and purity. We start the talk by motivating the need of such specific class of algebraic stacks which shall lead up to the construction of the stable homotopy functor and the four functors f^*, f_*, −⊗− and Hom(−,−). Then we briefly explain the construction of the exceptional functors, base change and projection formula using the so called ”Enhanced Operation Map” due to Liu and Zheng. The talk ends by stating the other properties of these six functors like localization and purity.

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EIMI, PDMI RAS and Chebyshev Laboratory

822 subscribers