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Article Dans Une Revue Advances in Mathematics Année : 2017

Dimensional homotopy t-structures in motivic homotopy theory

Résumé

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.

Dates et versions

hal-01659497 , version 1 (08-12-2017)

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