English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We apply Wildeshaus's theory of motivic intermediate extensions to themotivic decomposition conjecture, formulated by Deninger-Murre andCorti-Hanamura. We first obtain a general motivic decomposition for the Chowmotive of an arbitrary smooth projective family $f:X \rightarrow S$ whosegeometric fibers are Tate. Using Voevodsky's motives with rationalcoefficients, the formula is valid for an arbitrary regular base $S$, withoutassuming the existence of a base field or even of a prime integer $\ell$invertible on $S$. This result, and some of Bondarko' ideas, lead us to ageneralized formulation of Corti-Hanamura's conjecture. Secondly we establishthe existence of the motivic decomposition when $f:X \rightarrow S$ is aprojective quadric bundle over a characteristic $0$ base, which is eithersufficiently general or whose discriminant locus is a normal crossing divisor.This provides a motivic lift of the Bernstein-Beilinson-Deligne decompositionin this setting.

Motivic decompositions of families with Tate fibers: smooth and singular cases