1. Motivic Decompositions of Families With Tate Fibers: Smooth and Singular Cases.
- Author
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Cavicchi, M, Déglise, F, and Nagel, J
- Subjects
FIBERS ,FAMILIES ,INTEGERS ,LOGICAL prediction ,QUADRICS - Abstract
We apply Wildeshaus's theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by Deninger–Murre and Corti–Hanamura. We first obtain a general motivic decomposition for the Chow motive of an arbitrary smooth projective family |$f:X \rightarrow S$| whose geometric fibers are Tate. Using Voevodsky's motives with rational coefficients, the formula is valid for an arbitrary regular base |$S$| , without assuming the existence of a base field or even of a prime integer |$\ell $| invertible on |$S$|. This result, and some of Bondarko's ideas, lead us to a generalized formulation of Corti–Hanamura's conjecture. Secondly we establish the existence of the motivic decomposition when |$f:X \rightarrow S$| is a projective quadric bundle over a characteristic |$0$| base, which is either sufficiently general or whose discriminant locus is a normal crossing divisor. This provides a motivic lift of the Bernstein–Beilinson–Deligne decomposition in this setting. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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