Hida families, p -adic heights, and derivatives

Trevor Arnold[1]

  • [1] McMaster University Department of Mathematics & Statistics 1280 Main Street West Hamilton, ON L8S 4K1 (Canada)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 6, page 2275-2299
  • ISSN: 0373-0956

Abstract

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This paper concerns the arithmetic of certain p -adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a p -adic regulator, and the derivative of a p -adic L -function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first conjecture implies the equivalence of the last two.

How to cite

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Arnold, Trevor. "Hida families, $p$-adic heights, and derivatives." Annales de l’institut Fourier 60.6 (2010): 2275-2299. <http://eudml.org/doc/116333>.

@article{Arnold2010,
abstract = {This paper concerns the arithmetic of certain $p$-adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a $p$-adic regulator, and the derivative of a $p$-adic $L$-function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first conjecture implies the equivalence of the last two.},
affiliation = {McMaster University Department of Mathematics & Statistics 1280 Main Street West Hamilton, ON L8S 4K1 (Canada)},
author = {Arnold, Trevor},
journal = {Annales de l’institut Fourier},
keywords = {Iwasawa theory; Hida family; $p$-adic height; $p$-adic $L$-function; -adic height; -adic -function; Euler system},
language = {eng},
number = {6},
pages = {2275-2299},
publisher = {Association des Annales de l’institut Fourier},
title = {Hida families, $p$-adic heights, and derivatives},
url = {http://eudml.org/doc/116333},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Arnold, Trevor
TI - Hida families, $p$-adic heights, and derivatives
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 6
SP - 2275
EP - 2299
AB - This paper concerns the arithmetic of certain $p$-adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a $p$-adic regulator, and the derivative of a $p$-adic $L$-function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first conjecture implies the equivalence of the last two.
LA - eng
KW - Iwasawa theory; Hida family; $p$-adic height; $p$-adic $L$-function; -adic height; -adic -function; Euler system
UR - http://eudml.org/doc/116333
ER -

References

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