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2021 Lifting Chern classes by means of Ekedahl–Oort strata
Gerard van der Geer, Eduard Looijenga
Tunisian J. Math. 3(3): 469-480 (2021). DOI: 10.2140/tunis.2021.3.469

Abstract

The moduli space 𝒜g of principally polarized abelian varieties of genus g is defined over and admits a minimal compactification 𝒜g, also defined over . The Hodge bundle over 𝒜g has its Chern classes in the Chow ring of 𝒜g with -coefficients. We show that over 𝔽p, these Chern classes naturally lift to 𝒜g and do so in the best possible way: despite the highly singular nature of 𝒜g they are represented by algebraic cycles on 𝒜g𝔽p which define elements in the bivariant Chow ring. This is in contrast to the situation in the analytic topology, where these Chern classes have canonical lifts to the complex cohomology of the minimal compactification as Goresky–Pardon classes, which are known to define nontrivial Tate extensions inside the mixed Hodge structure on this cohomology.

Citation

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Gerard van der Geer. Eduard Looijenga. "Lifting Chern classes by means of Ekedahl–Oort strata." Tunisian J. Math. 3 (3) 469 - 480, 2021. https://doi.org/10.2140/tunis.2021.3.469

Information

Received: 3 January 2020; Revised: 20 June 2020; Accepted: 5 July 2020; Published: 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/tunis.2021.3.469

Subjects:
Primary: 11G18, 14G35

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.3 • No. 3 • 2021
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