Geometry of the eigencurve at critical Eisenstein series of weight 2

2013/07/18 by Majumdar, Dipramit
#11F #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1307.4846

Abstract

In this paper we show that the critical Eisenstein series of weight 2, E₂^crit_p, is smooth in the eigencurve C(l), where l is a prime. We also show that E₂^crit_p,ord_l is smooth in the full eigencurve C^full(l) and E₂^crit_p,ord_l₁,ord_l₂ is non-smooth in the full eigencurve C^full(l₁l₂). Further, we show that, E₂^crit_p, is étale over the weight space in the eigencurve C(l). As a consequence, we show that level lowering conjecture of Paulin fails to hold at E₂^crit_p,ord_l.

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