no. 7
Geometrie algébrique
A non-hyperelliptic curve with torsion Ceresa class
Beauville, Arnaud1 
1 Université Côte d’Azur, CNRS – Laboratoire J.-A. Dieudonné, Parc Valrose, F-06108 Nice cedex 2, France.
Comptes Rendus. Mathématique, Tome 359 (2021) no. 7, pp. 871-872.

We exhibit a non-hyperelliptic curve C of genus 3 such that the class of the Ceresa cycle [C]-[-C] in the intermediate Jacobian of JC is torsion.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.226
Beauville, Arnaud 1

1 Université Côte d’Azur, CNRS – Laboratoire J.-A. Dieudonné, Parc Valrose, F-06108 Nice cedex 2, France. 
@article{CRMATH_2021__359_7_871_0,
     author = {Beauville, Arnaud},
     title = {A non-hyperelliptic curve with torsion {Ceresa} class},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {871--872},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {7},
     year = {2021},
     doi = {10.5802/crmath.226},
     zbl = {07398739},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.226/}
}
TY  - JOUR
AU  - Beauville, Arnaud
TI  - A non-hyperelliptic curve with torsion Ceresa class
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 871
EP  - 872
VL  - 359
IS  - 7
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.226/
DO  - 10.5802/crmath.226
LA  - en
ID  - CRMATH_2021__359_7_871_0
ER  - 
%0 Journal Article
%A Beauville, Arnaud
%T A non-hyperelliptic curve with torsion Ceresa class
%J Comptes Rendus. Mathématique
%D 2021
%P 871-872
%V 359
%N 7
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.226/
%R 10.5802/crmath.226
%G en
%F CRMATH_2021__359_7_871_0
Beauville, Arnaud. A non-hyperelliptic curve with torsion Ceresa class. Comptes Rendus. Mathématique, Tome 359 (2021) no. 7, pp. 871-872. doi : 10.5802/crmath.226. http://www.numdam.org/articles/10.5802/crmath.226/

[1] Bisogno, Dean; Li, Wanlin; Litt, Daniel; Srinivasan, Padmavathi Group-theoretic Johnson classes and non-hyperelliptic curves with torsion Ceresa class (2020) (https://arxiv.org/abs/2004.06146)

[2] Ceresa, Giuseppe C is not algebraically equivalent to C - in its Jacobian, Ann. Math., Volume 117 (1983) no. 2, pp. 285-291 | DOI | MR | Zbl

[3] Fu, Lie; Laterveer, Robert; Vial, Charles Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type, Ann. Mat. Pura Appl. (4), Volume 200 (2021) no. 5, pp. 2085-2126 | Zbl

[4] Otsubo, Noriyuki On the Abel–Jacobi maps of Fermat Jacobians, Math. Z., Volume 270 (2012) no. 1-2, pp. 423-444 | DOI | Zbl

[5] Tadokoro, Yuuki A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic, Math. Z., Volume 260 (2008) no. 2, pp. 265-275 | DOI | MR | Zbl

Cité par Sources :