Kolyvagin's method for Chow groups of Kuga-Sato varieties over ring class fields

TL;DR

This paper extends Kolyvagin's method using Heegner cycles and Euler systems to bound Selmer groups of higher weight modular forms twisted by ring class characters, building on Nekovar's work.

Contribution

It introduces an extension of Nekovar's results by employing an Euler system of Heegner cycles for higher weight modular forms.

Findings

Bound the Selmer group associated to higher weight modular forms

Extend Nekovar's results using Heegner cycles

Refine Kolyvagin's ideas with Euler systems

Abstract

We use an Euler system of Heegner cycles to bound the Selmer group associated to a modular form of higher even weight twisted by a ring class character. This is an extension of Nekovar's result that uses Bertolini and Darmon's refinement of Kolyvagin's ideas.