### NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS

Achter JD, Casalaina-Martin S, Vial C (2019)
FORUM OF MATHEMATICS SIGMA 7: e36.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Achter, Jeffrey D.; Casalaina-Martin, Sebastian; Vial, CharlesUniBi
Einrichtung
Abstract / Bemerkung
For families of smooth complex projective varieties, we show that normal functions arising from algebraically trivial cycle classes are algebraic and defined over the field of definition of the family. In particular, the zero loci of those functions are algebraic and defined over such a field of definition. This proves a conjecture of Charles.
Erscheinungsjahr
2019
Zeitschriftentitel
FORUM OF MATHEMATICS SIGMA
Band
7
Art.-Nr.
e36
ISSN
2050-5094
Page URI
https://pub.uni-bielefeld.de/record/2946518

### Zitieren

Achter JD, Casalaina-Martin S, Vial C. NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS. FORUM OF MATHEMATICS SIGMA. 2019;7: e36.
Achter, J. D., Casalaina-Martin, S., & Vial, C. (2019). NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS. FORUM OF MATHEMATICS SIGMA, 7, e36. doi:10.1017/fms.2019.34
Achter, J. D., Casalaina-Martin, S., and Vial, C. (2019). NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS. FORUM OF MATHEMATICS SIGMA 7:e36.
Achter, J.D., Casalaina-Martin, S., & Vial, C., 2019. NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS. FORUM OF MATHEMATICS SIGMA, 7: e36.
J.D. Achter, S. Casalaina-Martin, and C. Vial, “NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS”, FORUM OF MATHEMATICS SIGMA, vol. 7, 2019, : e36.
Achter, J.D., Casalaina-Martin, S., Vial, C.: NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS. FORUM OF MATHEMATICS SIGMA. 7, : e36 (2019).
Achter, Jeffrey D., Casalaina-Martin, Sebastian, and Vial, Charles. “NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS”. FORUM OF MATHEMATICS SIGMA 7 (2019): e36.

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