Coleman Map in Coleman Families

2016/06/14 by Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Nuccio, Filippo A. E., Tadashi Ochiai +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1606.04441

Abstract

In this paper, we aimed at constructing a two-variable Coleman map for a given p-adic family of eigen cuspforms with a fixed non-zero slope (Coleman family). A Coleman map is a machinary which transforms a hypothetical p-adic family of zeta elements to a p-adic L-function. The result would be a non-ordinary generalization of a two-variable Coleman map for a given Hida deformation obtained by the second-named author.

Related

• Iwasawa Main Conjecture for p-adic families of elliptic modular cuspforms
• Nearly higher Coleman theory and p-adic L-functions for GSp(4) × GL(2) and GSp(4) × GL(2) × GL(2)
• p-adic rigidity of eigenforms of infinite slope
• Explicit Coleman integration for hyperelliptic curves
• Anticyclotomic p-adic L-functions for Coleman families of U_n+1 × U_n