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Geometriae Dedicata

, Volume 194, Issue 1, pp 1–28 | Cite as

Tautological rings on Jacobian varieties of curves with automorphisms

  • Thomas RichezEmail author
Original Paper Area 1

Abstract

Let J be the Jacobian of a smooth projective complex curve C which admits non-trivial automorphisms, and let \(\mathrm{{A}}(J)\) be the ring of algebraic cycles on J with rational coefficients modulo algebraic equivalence. We present new tautological rings in \(\mathrm{{A}}(J)\) which extend in a natural way the tautological ring studied by Beauville (Compos Math 140(3):683–688, 2004). We then show there exist tautological rings induced on special complementary abelian subvarieties of J.

Keywords

Algebraic cycles Tautological rings Jacobians Automorphisms Fourier transforms 

Mathematics Subject Classification (2010)

14C15 14C25 14H37 14H40 

Notes

Acknowledgements

This article is part of my thesis written at the University of Strasbourg. I would like to thank my Ph.D. advisor Professor Rutger Noot for his continual support and numerous suggestions which contributed to the improvement of this paper. I also want to thank the referee for his comments which helped me to reduce the length of this paper.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.CNRS, IRMA UMR 7501Université de StrasbourgStrasbourgFrance

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