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

2018/02/18 by Ochiai, Tadashi
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1802.06427

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).

Related

• The Iwasawa Main Conjectures for \rm GL₂ and derivatives of p-adic L-functions
• Coleman Map in Coleman Families
• Iwasawa theory for quadratic Hilbert modular forms
• Integral Iwasawa theory of Galois representations for non-ordinary primes
• A formal model of Coleman families and applications to Iwasawa invariants