Resumen de Big Heegner point Kolyvagin system for a family of modular forms

Kâzim Büyükboduk

• The principal goal of this paper is to develop Kolyvagin’s descent to apply with the big Heegner point Euler system constructed by Howard for the big Galois representation TT attached to a Hida family FF of elliptic modular forms. In order to achieve this, we interpolate and control the Tamagawa factors attached to each member of the family FF at bad primes, which should be of independent interest. Using this, we then work out the Kolyvagin descent on the big Heegner point Euler system so as to obtain a big Kolyvagin system that interpolates the collection of Kolyvagin systems obtained by Fouquet for each member of the family individually. This construction has standard applications to Iwasawa theory, which we record at the end.