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Dimensional homotopy t-structures in motivic homotopy theory.

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Τίτλος: Dimensional homotopy t-structures in motivic homotopy theory.
Συγγραφείς: Bondarko, Mikhail1, Déglise, Frédéric2
Πηγή: Advances in Mathematics. Apr2017, Vol. 311, p91-189. 99p.
Θεματικοί όροι: *Homotopy theory, *Spectral sequences (Mathematics), *Isomorphism (Mathematics), *Cohomology theory, *Sheaf theory
Περίληψη: 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. [ABSTRACT FROM AUTHOR]
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  – Url: https://www.doi.org/10.1016/j.aim.2017.02.003?
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  Data: Dimensional homotopy t-structures in motivic homotopy theory.
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  Data: 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. [ABSTRACT FROM AUTHOR]
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