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Third Italian Number Theory Meeting

Variation of anticyclotomic Iwasawa invariants in Hida families.

speaker: Matteo Longo (Università di Padova)

abstract: Given a modular form f and a quadratic imaginary field K, one can form a p-adic L-function interpolating central critical values of the complex L-function of f twisted by characters of the anticyclotomic Zp-extension of K. Under suitable parity conditions, one shows that this p-adic L-function is non-zero, and we can consider its mu and lambda Iwasawa invariants. When f lives in a Hida family, we show that these invariants are constants on branches, obtaining an anticyclotomic analogue of a similar result by Emerton-Pollack-Weston in the cyclotomic setting. This result allows us to spread results on the main conjecture from one form to all other forms in the family, obtaining new cases of the anticyclotomic main conjecture. This is a joint work with F. Castella and C.-H. Kim.

Tue 22 Sep, 10:50 - 11:40, Aula Dini
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