On endoscopic \(p\)-adic automorphic forms for \(\mathrm{SL}_2\). (English) Zbl 1441.11137
Summary: We show the existence of some non-classical cohomological \(p\)-adic automorphic eigenforms for \(\mathrm{SL}_2\) using endoscopy and the geometry of eigenvarieties. These forms seem to account for some non-automorphic members of classical global \(L\)-packets.
MSC:
| 11F85 | \(p\)-adic theory, local fields |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 14G22 | Rigid analytic geometry |
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