Dimensional homotopy t-structures in motivic homotopy theory

Abstract : The aim of this work is to construct certain homotopy t-structures on various categories of motivic homotopy theory, extending works of Voevodsky, Morel, Déglise and Ayoub. We prove these t-structures possess many good properties, some analogous to those of the perverse t-structure of Beilinson, Bernstein and Deligne. We compute the homology of certain motives, notably in the case of relative curves. We also show that the hearts of these t-structures provide convenient extensions of the theory of homotopy invariant sheaves with transfers, extending some of the main results of Voevodsky. These t-structures are closely related to Gersten weight structures as defined by Bondarko.
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https://hal.archives-ouvertes.fr/hal-01659497
Contributor : Imb - Université de Bourgogne <>
Submitted on : Friday, December 8, 2017 - 2:37:21 PM
Last modification on : Thursday, January 11, 2018 - 11:46:49 AM

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Mikhail Bondarko, Frédéric Déglise. Dimensional homotopy t-structures in motivic homotopy theory. Advances in Mathematics, Elsevier, 2017, 311, pp.91 - 189. ⟨10.1016/j.aim.2017.02.003⟩. ⟨hal-01659497⟩

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