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On refined nonvanishing conjectures by Kurihara and Kolyvagin
Francesc Castella, Takamichi Sano
In this paper, we extend the results of \cite{BCGS} on refined conjectures by Kurihara and Kolyvagin, allowing primes of any reduction type in the case of Kurihara's conjectures, a…
A formula of Perrin-Riou and characteristic power series of signed Selmer groups
Francesc Castella
We prove a conjecture of Kundu--Ray, following from the -adic Birch--Swinnerton-Dyer conjecture for supersingular primes by Bernardi--Perrin-Riou and Kato's Main Conjecture, pre…
Exceptional zeros for Heegner points and -converse to the theorem of Gross-Zagier and Kolyvagin
Francesc Castella
We prove a -converse to the theorem of Gross-Zagier and Kolyvagin for elliptic curves at primes of multiplicative reduction. Two key ingredients in the argu…
Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on
Francesc Castella, Zheng Liu, Xin Wan
In this paper we prove one side divisibility of the Iwasawa-Greenberg main conjecture for Rankin-Selberg product of a weight two cusp form and an ordinary CM form of higher weight,…
The Iwasawa Main Conjectures for and derivatives of -adic -functions
Francesc Castella, Xin Wan
We prove under mild hypotheses the three-variable Iwasawa main conjecture for -ordinary modular forms in the indefinite setting. Our result is in a setting complementary to that…
On anticyclotomic variants of the -adic Birch and Swinnerton-Dyer conjecture
Adebisi Agboola, Francesc Castella
We formulate analogues of the Birch and Swinnerton-Dyer conjecture for the -adic -functions of Bertolini-Darmon-Prasanna attached to elliptic curves at primes…