Parameter Spaces for Algebraic Equivalence

Achter JD, Casalaina-Martin S, Vial C (2019)
INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2019(6): 1863-1893.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Achter, Jeffrey D.; Casalaina-Martin, Sebastian; Vial, CharlesUniBi
Abstract / Bemerkung
A cycle is algebraically trivial if it can be exhibited as the difference of two fibers in a family of cycles parameterized by a smooth integral scheme. Over an algebraically closed field, it is a result of Weil that it suffices to consider families of cycles parameterized by curves, or by abelian varieties. In this article, we extend these results to arbitrary base fields. The strengthening of these results turns out to be a key step in our work elsewhere extending Murre's results on algebraic representatives for varieties over algebraically closed fields to arbitrary perfect fields.
Erscheinungsjahr
2019
Zeitschriftentitel
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Band
2019
Ausgabe
6
Seite(n)
1863-1893
ISSN
1073-7928
eISSN
1687-0247
Page URI
https://pub.uni-bielefeld.de/record/2936349

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Achter JD, Casalaina-Martin S, Vial C. Parameter Spaces for Algebraic Equivalence. INTERNATIONAL MATHEMATICS RESEARCH NOTICES. 2019;2019(6):1863-1893.
Achter, J. D., Casalaina-Martin, S., & Vial, C. (2019). Parameter Spaces for Algebraic Equivalence. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2019(6), 1863-1893. doi:10.1093/imrn/rnx178
Achter, J. D., Casalaina-Martin, S., and Vial, C. (2019). Parameter Spaces for Algebraic Equivalence. INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2019, 1863-1893.
Achter, J.D., Casalaina-Martin, S., & Vial, C., 2019. Parameter Spaces for Algebraic Equivalence. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2019(6), p 1863-1893.
J.D. Achter, S. Casalaina-Martin, and C. Vial, “Parameter Spaces for Algebraic Equivalence”, INTERNATIONAL MATHEMATICS RESEARCH NOTICES, vol. 2019, 2019, pp. 1863-1893.
Achter, J.D., Casalaina-Martin, S., Vial, C.: Parameter Spaces for Algebraic Equivalence. INTERNATIONAL MATHEMATICS RESEARCH NOTICES. 2019, 1863-1893 (2019).
Achter, Jeffrey D., Casalaina-Martin, Sebastian, and Vial, Charles. “Parameter Spaces for Algebraic Equivalence”. INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2019.6 (2019): 1863-1893.