Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes

Robert Harron[1]; Antonio Lei[2]

  • [1] Department of Mathematics Keller Hall University of Hawai‘i at Mānoa Honolulu, HI 96822, USA
  • [2] Département de mathématiques et de statistique Pavillon Alexandre-Vachon Université Laval Québec, QC Canada G1V 0A6

Journal de Théorie des Nombres de Bordeaux (2014)

  • Volume: 26, Issue: 3, page 673-707
  • ISSN: 1246-7405

Abstract

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Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p -adic L -functions for the symmetric powers of f , thus verifying conjectures of Dabrowski and Panchishkin in this special case. We combine this with recent work of Benois to prove the trivial zero conjecture in this setting. We also construct “mixed” plus and minus p -adic L -functions and prove an analogue of Pollack’s decomposition of the admissible p -adic L -functions. On the arithmetic side, we define corresponding mixed plus and minus Selmer groups and formulate the Main Conjecture of Iwasawa Theory.

How to cite

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Harron, Robert, and Lei, Antonio. "Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes." Journal de Théorie des Nombres de Bordeaux 26.3 (2014): 673-707. <http://eudml.org/doc/275790>.

@article{Harron2014,
abstract = {Let $f$ be a cuspidal newform with complex multiplication (CM) and let $p$ be an odd prime at which $f$ is non-ordinary. We construct admissible $p$-adic $L$-functions for the symmetric powers of $f$, thus verifying conjectures of Dabrowski and Panchishkin in this special case. We combine this with recent work of Benois to prove the trivial zero conjecture in this setting. We also construct “mixed” plus and minus $p$-adic $L$-functions and prove an analogue of Pollack’s decomposition of the admissible $p$-adic $L$-functions. On the arithmetic side, we define corresponding mixed plus and minus Selmer groups and formulate the Main Conjecture of Iwasawa Theory.},
affiliation = {Department of Mathematics Keller Hall University of Hawai‘i at Mānoa Honolulu, HI 96822, USA; Département de mathématiques et de statistique Pavillon Alexandre-Vachon Université Laval Québec, QC Canada G1V 0A6},
author = {Harron, Robert, Lei, Antonio},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
month = {12},
number = {3},
pages = {673-707},
publisher = {Société Arithmétique de Bordeaux},
title = {Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes},
url = {http://eudml.org/doc/275790},
volume = {26},
year = {2014},
}

TY - JOUR
AU - Harron, Robert
AU - Lei, Antonio
TI - Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2014/12//
PB - Société Arithmétique de Bordeaux
VL - 26
IS - 3
SP - 673
EP - 707
AB - Let $f$ be a cuspidal newform with complex multiplication (CM) and let $p$ be an odd prime at which $f$ is non-ordinary. We construct admissible $p$-adic $L$-functions for the symmetric powers of $f$, thus verifying conjectures of Dabrowski and Panchishkin in this special case. We combine this with recent work of Benois to prove the trivial zero conjecture in this setting. We also construct “mixed” plus and minus $p$-adic $L$-functions and prove an analogue of Pollack’s decomposition of the admissible $p$-adic $L$-functions. On the arithmetic side, we define corresponding mixed plus and minus Selmer groups and formulate the Main Conjecture of Iwasawa Theory.
LA - eng
UR - http://eudml.org/doc/275790
ER -

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