13 papers
Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes
Ashay Burungale, Shinichi Kobayashi, Kentaro Nakamura +1
We propose an integral framework for the anticyclotomic Iwasawa theory of CM elliptic curves at primes ramified in the CM field. The -constants of the geometri…
A refined non-vanishing of the -adic logarithm of a rational point on an abelian variety
Ashay Burungale, Christopher Skinner, Xin Wan
Inspired by a beautiful formula of Bertolini, Darmon, and Prasanna -- the oft-termed BDP formula -- we address questions about the non-vanishing of non-torsion points under -adi…
Anticyclotomic Iwasawa theory of abelian varieties of -type at non-ordinary primes II
Ashay Burungale, Kâzım Büyükboduk, Antonio Lei
Let an elliptic curve with good supersingular reduction at a prime , and an imaginary quadratic field such that the root number of over equals $…
Mod non-vanishing of self-dual Hecke -values over CM fields and applications
Ashay Burungale, Wei He, Ye Tian +1
Let be a self-dual Hecke character over a CM field . Let be a degree one prime of the maximal totally real subfield of and the Ga…
Non-vanishing of Kolyvagin systems and Iwasawa theory
Ashay Burungale, Francesc Castella, Giada Grossi +1
Let be an elliptic curve and an odd prime. In 1991 Kolyvagin conjectured that the system of cohomology classes for torsion quotients of the -adic Tate module…
Hecke -values, definite Shimura sets and Mod non-vanishing
Ashay A. Burungale, Wei He, Shinichi Kobayashi +1
Let be a self-dual Hecke character over an imaginary quadratic field of infinity type . Let and be primes which are coprime to $6N_{K/\mathbb{Q}}({\mathr…