p-adic deformations of Saito-Kurokawa lifts

Christopher Skinner; Eric Urban

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

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.

Original language	English (US)
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

General Mathematics

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

Cite this

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title = "p-adic deformations of Saito-Kurokawa lifts",

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.",

author = "Christopher Skinner and Eric Urban",

year = "2002",

month = oct,

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doi = "10.1016/S1631-073X(02)02540-2",

language = "English (US)",

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T1 - p-adic deformations of Saito-Kurokawa lifts

AU - Skinner, Christopher

AU - Urban, Eric

PY - 2002/10/1

Y1 - 2002/10/1

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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U2 - 10.1016/S1631-073X(02)02540-2

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

M3 - Article

AN - SCOPUS:0037715290

SN - 1631-073X

VL - 335

SP - 581

EP - 586

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 7

ER -

p-adic deformations of Saito-Kurokawa lifts

Abstract

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