Comptes Rendus
no. 7-8
Algebraic Geometry/Number Theory
Essential dimension of Abelian varieties over number fields
Presented by: Jean-Pierre Serre
Patrick Brosnan1; Ramesh Sreekantan2
1 Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., Canada V6T 1Z2
2 School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai 400 005, India
Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 417-420

We show that the essential dimension of a non-trivial Abelian variety over a number field is infinite.

On montre que la dimension essentielle d'une variété abélienne non-triviale définie sur un corps de nombres est infinie.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.02.008

Patrick Brosnan 1; Ramesh Sreekantan 2

1 Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., Canada V6T 1Z2
2 School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai 400 005, India 
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Patrick Brosnan; Ramesh Sreekantan. Essential dimension of Abelian varieties over number fields. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 417-420. doi: 10.1016/j.crma.2008.02.008

[1] G. Berhuy; G. Favi Essential dimension: a functorial point of view (after A. Merkurjev), Doc. Math., Volume 8 (2003), pp. 279-330 (electronic)

[2] P. Brosnan The essential dimension of a g-dimensional complex abelian variety is 2g, Transform. Groups, Volume 12 (2007) no. 3, pp. 437-441

[3] P. Brosnan; Z. Reichstein; A. Vistoli Essential dimension and algebraic stacks | arXiv

[4] W.C. Chi l-adic and λ-adic representations associated to abelian varieties defined over number fields, Amer. J. Math., Volume 114 (1992) no. 2, pp. 315-353

[5] P. Deligne; J.S. Milne; A. Ogus; K.-y. Shih Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Mathematics, vol. 900, Springer-Verlag, Berlin, 1982

[6] M. Florence On the essential dimension of cyclic p-groups, Invent. Math., Volume 171 (2008) no. 1, pp. 175-189

[7] N. Karpenko A. Merkurjev, Essential dimension of finite p-groups, Invent. Math., Online first. DOI: | DOI

[8] J.-P. Serre Abelian l-adic Representations and Elliptic Curves, Research Notes in Mathematics, vol. 7, A K Peters Ltd., Wellesley, MA, 1998 (With the collaboration of Willem Kuyk and John Labute, Revised reprint of the 1968 original)

[9] J.-P. Serre Letter to K. Ribet dated 1.1.1981, Œuvres. Collected Papers, IV, Springer-Verlag, Berlin, 2000, pp. 1985-1998 (pp. viii+657)

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