This paper proves a version of Iwasawa's Main Conjecture for the anticyclotomic p-adic L-function attached to an elliptic curve E over the rationals and to an imaginary quadratic field K. More specifically, when p is an ordinary prime for E, it shows that the characteristic power series of the Pontrjagin-dual of the pro-p Selmer group of E over the anticyclotomic Z_p-extension of K divides the anticyclotomic p-adic L-function. The proof combines the theory of congruences between modular forms with the Cerednik-Drinfeld theory of p-adic uniformisation of Shimura curves and the theory of complex multiplication of abelian varieties.

Iwasawa's Main Conjecture for elliptic curves over anticyclotomic $\Z_p$-extensions / M. Bertolini, H. Darmon. - In: ANNALS OF MATHEMATICS. - ISSN 0003-486X. - 162:1(2005), pp. 1-64.

Iwasawa's Main Conjecture for elliptic curves over anticyclotomic $\Z_p$-extensions

M. Bertolini;
2005

Abstract

This paper proves a version of Iwasawa's Main Conjecture for the anticyclotomic p-adic L-function attached to an elliptic curve E over the rationals and to an imaginary quadratic field K. More specifically, when p is an ordinary prime for E, it shows that the characteristic power series of the Pontrjagin-dual of the pro-p Selmer group of E over the anticyclotomic Z_p-extension of K divides the anticyclotomic p-adic L-function. The proof combines the theory of congruences between modular forms with the Cerednik-Drinfeld theory of p-adic uniformisation of Shimura curves and the theory of complex multiplication of abelian varieties.
main conjecture ; Iwasawa theory ; p-adic L-functions
Settore MAT/03 - Geometria
2005
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/14657
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