Guletskiĭ, Vladimir
(2018)
Chow motives of abelian type over a base.
European Journal of Mathematics, 4 (3).
pp. 1065-1086.
Text
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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 |
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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: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3030225 |