CM cycles on Kuga–Sato varieties over Shimura curves and Selmer groups

Elias, Yara ; de Vera-Piquero, Carlos

Resumen: Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga–Sato variety over a suitable Shimura curve which gives rise to a system of Galois cohomology classes attached to f enjoying the compatibility properties of an Euler system. Then we use Kolyvagin’s method, as adapted by Nekovář to higher weight modular forms, to bound the size of the relevant Selmer group associated to f and K and prove the finiteness of the (primary part) of the Shafarevich–Tate group, provided that a suitable cohomology class does not vanish.

Idioma: Inglés

DOI: 10.1515/forum-2017-0008

Año: 2018

Publicado en: Forum mathematicum 30, 2 (2018), 321-346
ISSN: 0933-7741

Factor impacto JCR: 0.867 (2018)

Categ. JCR: MATHEMATICS rank: 120 / 313 = 0.383 (2018) - Q2 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 170 / 254 = 0.669 (2018) - Q3 - T3

Factor impacto SCIMAGO: 0.898 - Mathematics (miscellaneous) (Q1) - Applied Mathematics (Q1)

Tipo y forma: Article (PostPrint)