Chow motives of abelian type over a base

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

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© 2018, The Author(s). 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 Sym d-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
Depositing User: Symplectic Admin
Date Deposited: 19 Dec 2018 10:55
Last Modified: 14 Jun 2019 10:10
DOI: 10.1007/s40879-018-0270-9
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