On anticyclotomic Euler and Kolyvagin systems

Abstract

We introduce an axiomatization of the notion of ( $p$-complete) anticyclotomic Euler system for a wide class of Galois representations, including those attached to a cuspidal eigenform and to a Hida family of modular forms. Under a minimal set of assumptions, we show how to build from these data a universal Kolyvagin system for the representation and for its anticyclotomic twist. Eventually, we recover some applications to the structure of Selmer groups and Iwasawa main conjectures and we review a few concrete examples of these abstract notions that can be found in the literature.

arXiv comment38 pages; to appear in Ann. Math. Qué

References in corpus (5)

• Variation of Heegner points in Hida families
• Heegner points in Coleman families
• Kolyvagin systems and Iwasawa theory of generalized Heegner cycles
• Big Heegner point Kolyvagin system for a family of modular forms
• On the structure of the Bloch--Kato Selmer groups of modular forms over anticyclotomic ${\mathbf{Z}}_p$-towers