Let A/Q be a modular abelian variety attached to a weight 2 new modular form of level N=pM, where p is a prime and M is an integer prime to p. When K/Q is an imaginary quadratic extension the Heegner points, that are defined over the ring class fields H/K, can contribute to the growth of the rank of the Selmer groups over H. When K/Q is a real quadratic field the theory of Stark-Heegner points provides a conjectural explanation of the growth of these ranks under suitable sign conditions on the L-function of f/K. The main result of the paper relates the growth of the Selmer groups to the conjectured rationality of the Stark-Heegner points over the expected field of definition.
Congruences and rationality of Stark-Heegner points / M.A. Seveso. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 132:3(2012), pp. 414-447.
Congruences and rationality of Stark-Heegner points
M.A. SevesoPrimo
2012
Abstract
Let A/Q be a modular abelian variety attached to a weight 2 new modular form of level N=pM, where p is a prime and M is an integer prime to p. When K/Q is an imaginary quadratic extension the Heegner points, that are defined over the ring class fields H/K, can contribute to the growth of the rank of the Selmer groups over H. When K/Q is a real quadratic field the theory of Stark-Heegner points provides a conjectural explanation of the growth of these ranks under suitable sign conditions on the L-function of f/K. The main result of the paper relates the growth of the Selmer groups to the conjectured rationality of the Stark-Heegner points over the expected field of definition.Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.