On the image of Λ -adic Galois representations

Ami Fischman[1]

  • [1] 517 N 137th Street, Seattle WA 98133 (USA)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 2, page 351-378
  • ISSN: 0373-0956

Abstract

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We explore the question of how big the image of a Galois representation attached to a Λ -adic modular form with no complex multiplication is and show that for a “generic” set of Λ -adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.

How to cite

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Fischman, Ami. "On the image of $\Lambda $-adic Galois representations." Annales de l’institut Fourier 52.2 (2002): 351-378. <http://eudml.org/doc/115983>.

@article{Fischman2002,
abstract = {We explore the question of how big the image of a Galois representation attached to a $\Lambda $-adic modular form with no complex multiplication is and show that for a “generic” set of $\Lambda $-adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.},
affiliation = {517 N 137th Street, Seattle WA 98133 (USA)},
author = {Fischman, Ami},
journal = {Annales de l’institut Fourier},
keywords = {modular form; $p$-adic family; Galois representation; $p$-adic modular form; -adic family; -adic modular form},
language = {eng},
number = {2},
pages = {351-378},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the image of $\Lambda $-adic Galois representations},
url = {http://eudml.org/doc/115983},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Fischman, Ami
TI - On the image of $\Lambda $-adic Galois representations
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 2
SP - 351
EP - 378
AB - We explore the question of how big the image of a Galois representation attached to a $\Lambda $-adic modular form with no complex multiplication is and show that for a “generic” set of $\Lambda $-adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.
LA - eng
KW - modular form; $p$-adic family; Galois representation; $p$-adic modular form; -adic family; -adic modular form
UR - http://eudml.org/doc/115983
ER -

References

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  13. B. Mazur, A. Wiles, On p-adic analytic families of Galois representations, Compositio Math. 59 (1986), 231-264 Zbl0654.12008MR860140
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