Sur les déformations p-adiques des formes de Saito-Kurokawa

Christopher Skinner; Eric Urban

doi:10.1016/S1631-073X(02)02540-2

Sur les déformations p-adiques des formes de Saito-Kurokawa

Translated title of the contribution: p-adic deformations of Saito-Kurokawa lifts

Christopher Skinner, Eric Urban

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Let f be a cuspidal eigenform of weight 2k - 2 ≥ 2 and level 1. Suppose p is an ordinary prime for f and V_f is the p-adic representation of weight 2k - 3 associated to f. We show that if the zeta function of f vanishes at s = k - 1 to odd order, then the Selmer group H_f¹ (ℚ V_f (k - 1)) is infinite.

Translated title of the contribution	p-adic deformations of Saito-Kurokawa lifts
Original language	French
Pages (from-to)	581-586
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	335
Issue number	7
DOIs	https://doi.org/10.1016/S1631-073X(02)02540-2
State	Published - Oct 1 2002
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1016/S1631-073X(02)02540-2

Cite this

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abstract = "Let f be a cuspidal eigenform of weight 2k - 2 ≥ 2 and level 1. Suppose p is an ordinary prime for f and Vf is the p-adic representation of weight 2k - 3 associated to f. We show that if the zeta function of f vanishes at s = k - 1 to odd order, then the Selmer group Hf1 (ℚ Vf (k - 1)) is infinite.",

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N2 - Let f be a cuspidal eigenform of weight 2k - 2 ≥ 2 and level 1. Suppose p is an ordinary prime for f and Vf is the p-adic representation of weight 2k - 3 associated to f. We show that if the zeta function of f vanishes at s = k - 1 to odd order, then the Selmer group Hf1 (ℚ Vf (k - 1)) is infinite.

AB - Let f be a cuspidal eigenform of weight 2k - 2 ≥ 2 and level 1. Suppose p is an ordinary prime for f and Vf is the p-adic representation of weight 2k - 3 associated to f. We show that if the zeta function of f vanishes at s = k - 1 to odd order, then the Selmer group Hf1 (ℚ Vf (k - 1)) is infinite.

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Sur les déformations p-adiques des formes de Saito-Kurokawa

Abstract

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