Endoscopic points on the SL(2)-eigencurve

Abstract: After recalling some background on Langlands correspondences and $L$-packets for $\mathrm{SL}(2)$, we will study endoscopy in the setting of eigenvarietes. I will explain the existence of some interesting $p$-adic automorphic forms that can be seen using the $\mathrm{SL}(2)$-eigencurve at certain endoscopic points. Finally I will report on work in progress with C. Johansson, where we study the $\mathrm{SL}(2)$-eigencurve at endoscopic points via the Coleman-Mazur eigencurve.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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