Comptes Rendus
no. 23-24
Number Theory/Dynamical Systems
Towards an effective version of Mazur conjecture
[Vers une version effective de la conjecture de Mazur]

Présenté par : Jean-Pierre Serre

Nicolas Templier1
1 Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1245-1247.

Dans cette Note on présente une vue axiomatique de l'argument principal de la démonstration par Cornut–Vatsal de la conjecture de Mazur. Notre objectif est d'extraire des énoncés ergodiques clairs et de discuter une possible stratégie vers une version effective.

In this Note we present an axiomatic exposition of Cornut–Vatsal's main ingredient in their proof of Mazur conjecture. Our aim is to extract clean ergodic statements and discuss a possible strategy towards effectivity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.011
Nicolas Templier 1

1 Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA 
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Nicolas Templier. Towards an effective version of Mazur conjecture. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1245-1247. doi : 10.1016/j.crma.2010.10.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.011/

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[2] C. Cornut Normes p-adiques et extensions quadratiques, Ann. Inst. Fourier, Volume 59 (2009), pp. 2223-2254

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[4] C. Cornut; V. Vatsal Nontriviality of Rankin–Selberg L-functions and CM points, L-Functions and Galois Representations, London Math. Soc. Lecture Note Ser., vol. 320, Cambridge Univ. Press, Cambridge, 2007, pp. 121-186

[5] G.A. Margulis; G.M. Tomanov Invariant measures for actions of unipotent groups over local fields on homogeneous spaces, Invent. Math., Volume 116 (1994) no. 1–3, pp. 347-392

[6] B. Mazur Modular curves and arithmetic, Warsaw, 1983, PWN, Warsaw (1984), pp. 185-211

[7] M. Ratner Raghunathan's conjectures for Cartesian products of real and p-adic Lie groups, Duke Math. J., Volume 77 (1995) no. 2, pp. 275-382

[8] N. Shah Unipotent flows on products of SL(2,K)/Γ's, Séminaires et congrès, Volume 22 (2009), pp. 71-106

[9] V. Vatsal Special values of anticyclotomic L-functions, Duke Math. J., Volume 116 (2003) no. 2, pp. 219-261

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