Chow motives of abelian type over a base

Guletskiĭ, Vladimir (2018) Chow motives of abelian type over a base. European Journal of Mathematics, 4 (3). pp. 1065-1086.

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Abstract

Let S be a Noetherian scheme, let X be a smooth projective scheme over S, whose fibres are connected curves of genus g, and let J be the Jacobian scheme of the relative curve X over S. We generalise the theorem due to Rolph Schwarzenberger and prove that if S is integral and normal, and the structural morphism admits a section, then there exists a locally free sheaf [InlineEquation not available: see fulltext.] on J, such that the relative symmetric power [InlineEquation not available: see fulltext.] is isomorphic to the projective bundle [InlineEquation not available: see fulltext.] over J, provided [InlineEquation not available: see fulltext.], and the ample divisor is Symd-1(X/ S) , embedded into [InlineEquation not available: see fulltext.] by the section of the structural morphism from X to S. Then we use this result to generalise the theorem due to Shun-Ichi Kimura: if S is an integral regular scheme, separated and of finite type over a Dedekind domain, then all relative Chow motives of abelian type over S are finite-dimensional.

Item Type:	Article
Uncontrolled Keywords:	Relative curves, Jacobian scheme, Picard bundles, Symmetric powers, Riemann–Roch theorem, Chow motives
Depositing User:	Symplectic Admin
Date Deposited:	19 Dec 2018 10:55
Last Modified:	19 Jan 2023 01:08
DOI:	10.1007/s40879-018-0270-9
Open Access URL:	http://pcwww.liv.ac.uk/~guletski/papers/chowmotive...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3030225