On Endoscopic $p$-Adic Automorphic Forms for $\mathrm{SL}_2$

Judith Ludwig

doi:10.4171/dm/622

JournalsdmVol. 23pp. 383–406

On Endoscopic $p$ -Adic Automorphic Forms for $SL_{2}$

Judith Ludwig
Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany

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Abstract

We show the existence of some non-classical cohomological $p$ -adic automorphic eigenforms for $SL_{2}$ using endoscopy and the geometry of eigenvarieties. These forms seem to account for some non-automorphic members of classical global $L$ -packets.

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Judith Ludwig, On Endoscopic $p$ -Adic Automorphic Forms for $SL_{2}$ . Doc. Math. 23 (2018), pp. 383–406

DOI 10.4171/DM/622