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arXiv 2011.065792020-11math.NT

A geometric view on Iwasawa theory

Adel Betina, Mladen Dimitrov

备注：: to appear in J. Th. Nombres Bordeaux (Iwasawa 2019 special issue)

英文摘要：

This article extends our study of the geometry of the $p$-adic eigencurve at a point defined by a weight $1$ cuspform $f$ irregular at $p$ and having complex multiplication, and the implications in Iwasawa and in Hida theories. The novel results include the determination of the Fourier coefficients of certain non-classical $p$-adic modular forms belonging to the generalized eigenspace of $f$, in terms of $p$-adic logarithms of algebraic numbers. We also compute the "mysterious" cross-ratios of the $p$-ordinary filtrations of the Hida families containing $f$.

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