2014/05/12 by Matteo Longo, Longo, Matteo, Stefano Vigni +1
Mathematics · #11F11 #11R23 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11F11 #msc:11R23
paper · pdf · doi:10.48550/arxiv.1405.2777
Minor modifications; 27 pages
arxiv created 2014/05/19 · arxiv updated 2014/05/20
Iwasawa theory of Heegner points on abelian varieties of GL2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper, the first in a series of two, is to describe extensions of some of their results in which abelian varieties are replaced by the Galois cohomology of Deligne's p-adic representation attached to a modular form f of even weight >2. In this more general setting, the role of Heegner points is played by higher-dimensional Heegner cycles in the sense of Nekovář. In particular, we prove that the Pontryagin dual of a certain Bloch-Kato Selmer group associated with f has rank 1 over a suitable anticyclotomic Iwasawa algebra.