Quelques courbes de Hecke se plongent dans l'espace de Colmez

TL;DR

This paper proves that for primes 2, 3, 5, and 7, the p-adic Eigencurve is isomorphic to a certain blow-up of the Fredholm hypersurface, revealing a deep geometric connection.

Contribution

It establishes a rigid-analytic isomorphism between the p-adic Eigencurve and a blow-up of the Fredholm hypersurface at special points for specific primes.

Findings

C is isomorphic to Z for p=2,3,5,7

The map C -> Z is a rigid-analytic isomorphism in these cases

Provides geometric insight into the structure of the Eigencurve

Abstract

Let p be a prime, C the p-adic Eigencurve (with tame level 1) and Z the blow-up of the Fredholm hypersurface of the U_p - operator at the special points. We show that for p = 2, 3, 5 and 7, the natural map C -> Z is a rigid-analytic isomorphism.