# 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

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topArnold, 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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