Iwasawa theory for elliptic curves over imaginary quadratic fields

Massimo Bertolini

Journal de théorie des nombres de Bordeaux (2001)

  • Volume: 13, Issue: 1, page 1-25
  • ISSN: 1246-7405

Abstract

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Let E be an elliptic curve over ℚ , let K be an imaginary quadratic field, and let K ∞ be a ℤ p -extension of K . Given a set Σ of primes of K , containing the primes above p , and the primes of bad reduction for E , write K Σ for the maximal algebraic extension of K which is unramified outside Σ . This paper is devoted to the study of the structure of the cohomology groups H i ( K Σ / K ∞ , E p ∞ ) for i = 1 , 2 , and of the p -primary Selmer group Sel p ∞ ( E / K ∞ ) , viewed as discrete modules over the Iwasawa algebra of K ∞ / K .

How to cite

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Bertolini, Massimo. "Iwasawa theory for elliptic curves over imaginary quadratic fields." Journal de théorie des nombres de Bordeaux 13.1 (2001): 1-25. <http://eudml.org/doc/248714>.

@article{Bertolini2001,
abstract = {Let $E$ be an elliptic curve over $\mathbb \{Q\}$, let $K$ be an imaginary quadratic field, and let $K_ \infty $ be a $\mathbb \{Z\}_p$-extension of $K$. Given a set $\Sigma $ of primes of $K$, containing the primes above $p$, and the primes of bad reduction for $E$, write $K_\Sigma $ for the maximal algebraic extension of $K$ which is unramified outside $\Sigma $. This paper is devoted to the study of the structure of the cohomology groups $H^i (K_\Sigma / K_\infty , E_\{p^ \infty \})$ for $i = 1, 2,$ and of the $p$-primary Selmer group Sel$_\{p^ \infty \}(E / K_\infty )$, viewed as discrete modules over the Iwasawa algebra of $K_\infty / K.$},
author = {Bertolini, Massimo},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {elliptic curve; Selmer group; anticyclotomic extension; Iwasawa theory; complex multiplication; Heegner points},
language = {eng},
number = {1},
pages = {1-25},
publisher = {Université Bordeaux I},
title = {Iwasawa theory for elliptic curves over imaginary quadratic fields},
url = {http://eudml.org/doc/248714},
volume = {13},
year = {2001},
}

TY - JOUR
AU - Bertolini, Massimo
TI - Iwasawa theory for elliptic curves over imaginary quadratic fields
JO - Journal de théorie des nombres de Bordeaux
PY - 2001
PB - Université Bordeaux I
VL - 13
IS - 1
SP - 1
EP - 25
AB - Let $E$ be an elliptic curve over $\mathbb {Q}$, let $K$ be an imaginary quadratic field, and let $K_ \infty $ be a $\mathbb {Z}_p$-extension of $K$. Given a set $\Sigma $ of primes of $K$, containing the primes above $p$, and the primes of bad reduction for $E$, write $K_\Sigma $ for the maximal algebraic extension of $K$ which is unramified outside $\Sigma $. This paper is devoted to the study of the structure of the cohomology groups $H^i (K_\Sigma / K_\infty , E_{p^ \infty })$ for $i = 1, 2,$ and of the $p$-primary Selmer group Sel$_{p^ \infty }(E / K_\infty )$, viewed as discrete modules over the Iwasawa algebra of $K_\infty / K.$
LA - eng
KW - elliptic curve; Selmer group; anticyclotomic extension; Iwasawa theory; complex multiplication; Heegner points
UR - http://eudml.org/doc/248714
ER -

References

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