Coleman Maps for Modular Forms at Supersingular Primes over Lubin-Tate Extensions

TL;DR

This paper extends the construction of Coleman maps, originally for elliptic curves with supersingular reduction, to modular forms of higher weights over Lubin-Tate extensions, broadening the scope of Iovita and Pollack's work.

Contribution

It generalizes the Coleman maps from elliptic curves to higher weight modular forms over Lubin-Tate extensions, expanding their applicability.

Findings

Constructed Coleman maps for higher weight modular forms.

Extended Iovita and Pollack's framework to new settings.

Provides tools for studying Selmer groups in this context.

Abstract

Given an elliptic curve with supersingular reduction at an odd prime p, Iovita and Pollack have generalised results of Kobayashi to define even and odd Coleman maps at p over Lubin-Tate extensions given by a formal group of height 1. We generalise this construction to modular forms of higher weights.