Variation of anticyclotomic Iwasawa invariants in Hida families Article Swipe

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Conjecture Variation (astronomy) Mathematics Pure mathematics Yield (engineering) Iwasawa theory Algebra over a field Physics Astrophysics Thermodynamics

Francesc Castella , Chan-Ho Kim , Matteo Longo ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.2140/ant.2017.11.2339 · OA: W1739655987

Building on the construction of big Heegner points in the quaternionic setting, and their relation to special values of Rankin-Selberg $L$-functions, we obtain anticyclotomic analogues of the results of Emerton-Pollack-Weston on the variation of Iwasawa invariants in Hida families. In particular, combined with the known cases of the anticyclotomic Iwasawa main conjecture in weight $2$, our results yield a proof of the main conjecture for $p$-ordinary newforms of higher weights and trivial nebentypus.