Comptes Rendus
no. 6
Number theory/Algebraic geometry
Ordinary primes for Abelian surfaces

Presented by: Jean-Pierre Serre

William F. Sawin1
1 Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, USA
Comptes Rendus. Mathématique, Volume 354 (2016) no. 6, pp. 566-568.

We compute the density of the set of ordinary primes of an Abelian surface over a number field in terms of the ℓ-adic monodromy group.

On étudie la densité de l'ensemble des places ordinaires pour une surface abélienne sur un corps de nombres, en se servant du groupe de monodromie ℓ-adique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.01.025

William F. Sawin 1

1 Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, USA 
@article{CRMATH_2016__354_6_566_0,
     author = {William F. Sawin},
     title = {Ordinary primes for {Abelian} surfaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {566--568},
     publisher = {Elsevier},
     volume = {354},
     number = {6},
     year = {2016},
     doi = {10.1016/j.crma.2016.01.025},
     language = {en},
}
TY  - JOUR
AU  - William F. Sawin
TI  - Ordinary primes for Abelian surfaces
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 566
EP  - 568
VL  - 354
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2016.01.025
LA  - en
ID  - CRMATH_2016__354_6_566_0
ER  - 
%0 Journal Article
%A William F. Sawin
%T Ordinary primes for Abelian surfaces
%J Comptes Rendus. Mathématique
%D 2016
%P 566-568
%V 354
%N 6
%I Elsevier
%R 10.1016/j.crma.2016.01.025
%G en
%F CRMATH_2016__354_6_566_0
William F. Sawin. Ordinary primes for Abelian surfaces. Comptes Rendus. Mathématique, Volume 354 (2016) no. 6, pp. 566-568. doi : 10.1016/j.crma.2016.01.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.025/

[1] N. Bourbaki Lie Groups and Lie Algebras III, Springer, 1975

[2] P. Deligne Variétés abéliennes ordinaires sur un corps fini, Invent. Math., Volume 8 (1969), pp. 238-243

[3] G. Faltings Finiteness theorems for Abelian varieties over number fields (G. Cornell; J.H. Silverman, eds.), Arithmetic Geometry, Springer-Verlag, 1986, pp. 9-26

[4] F. Fité; K.S. Kedlaya; V. Rotger; A.V. Sutherland Sato–Tate distributions and Galois endomorphism modules in genus 2, Compos. Math., Volume 148 (2012), pp. 1390-1442

[5] A. Ogus Hodge cycles and crystalline cohomology, Hodge Cycles, Motives, and Shimura Varieties, Springer Lecture Notes in Mathematics, vol. 900, Springer-Verlag, 1982, pp. 357-414

[6] R. Pink ℓ-adic algebraic monodromy groups, cocharacters, and the Mumford–Tate conjecture, J. Reine Angew. Math., Volume 495 (1998), pp. 187-237

[7] J.-P. Serre Représentations ℓ-adiques, Kyoto Symposium on Algebraic Number Theory, Japan Society for the Promotion of Science, 1977, pp. 177-193

[8] J.-P. Serre Lectures on NX(p), Research Notes in Mathematics, A K Peters/CRC Press, 2011

Cited by Sources:

Comments - Policy