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arXiv · 1802.06427

Iwasawa Main Conjecture for $p$-adic families of elliptic modular cuspforms

Tadashi Ochiai
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Abstract

In this article, we discuss Iwasawa Main Conjecture for $p$-adic families of elliptic modular cuspforms. After the overview on the situation of the ordinary case of Hida family, we will introduce a Coleman map for Coleman family for the non-ordinary case (Coleman family) which was obtained as a joint work with Filippo Nuccio [NO16] and we give some results on Iwasawa Theory for Coleman families as applications of . First, we give a construction of a two-variable $p$-adic $L$-function for a Coleman family thanks to the ingredients given in [NO16] (Theorem 5.1). Combining this result and Coleman map obtained in [NO16], we also construct Beilinson-Kato Euler systems over a Coleman family (Thorem 5.3). Finally we formulate Iwasawa Main conjecture for a Coleman family and prove the half of Iwasawa Main Conjecture (Theorem 5.6).

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BibTeXRIS

Tadashi Ochiai. 2018-02-18. Iwasawa Main Conjecture for $p$-adic families of elliptic modular cuspforms. https://arxiv.org/abs/1802.06427

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