Séminaire Exposé exceptionnel
organisé par l'équipe
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Swann Tubach
Realization of motives and mixed Hodge modules on stacks -- 1
26 mai 2025 - 10:00Salle de conférences IRMA
(Mini-course in the context of ANR-DAGART) The goal of the course is to explain the construction of the Hodge realisation of relative motives. To do so, we will begin by doing some recollections on perverse sheaves, 6 operations, mixed Hodge modules and motives. Using the operations, we will prove that mixed Hodge modules have an oo-categorical enhancement, by doing a "change of variables": the derived category of mixed Hodge modules is also the derived category of "constructible mixed Hodge modules". We will explain the universal property of motives and use it to show that the enhancement implies the existence of a Hodge realisation of motives, compatible with the 6 operations. The enhancement can also be used to extend mixed Hodge modules to algebraic stacks. We will finish the course by constructing the vanishing cycles functor for mixed Hodge modules on stacks relying on a Koszul duality interpretation.
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Swann Tubach
Realization of motives and mixed Hodge modules on stacks -- 2
28 mai 2025 - 10:00Salle de séminaires IRMA
(Mini-course in the context of ANR-DAGART) The goal of the course is to explain the construction of the Hodge realisation of relative motives. To do so, we will begin by doing some recollections on perverse sheaves, 6 operations, mixed Hodge modules and motives. Using the operations, we will prove that mixed Hodge modules have an oo-categorical enhancement, by doing a "change of variables": the derived category of mixed Hodge modules is also the derived category of "constructible mixed Hodge modules". We will explain the universal property of motives and use it to show that the enhancement implies the existence of a Hodge realisation of motives, compatible with the 6 operations. The enhancement can also be used to extend mixed Hodge modules to algebraic stacks. We will finish the course by constructing the vanishing cycles functor for mixed Hodge modules on stacks relying on a Koszul duality interpretation.
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Richard Crew
Weil Groups and F-isocrystals
28 mai 2025 - 15:30Salle de séminaires IRMA
Résumé en anglais : We give an explicit construction of the fundamental class of a Galois extension of local fields, based on the Dieudonne-Manin structure theorem for F-isocrystals. This makes possible an elementary derivation of the basic results of local class field theory.