Rigid inner forms vs isocrystals. (English) Zbl 1430.11071
Summary: We compare two statements of the refined local Langlands correspondence for connected reductive groups defined over a \(p\)-adic field: one involving Kottwitz’s set \(B(G)\) of isocrystals with additional structure, and one involving the cohomology set \(H^1(u\to W,Z\to G)\) of
[the author, Ann. Math. (2) 184, No. 2, 559–632 (2016; Zbl 1393.22009)]. We show that if either statement is valid for all connected reductive groups, then so is the other. We also discuss how the second statement depends on the choice of an element of \(H^1(u\to W,Z\to G\)).
MSC:
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 11S37 | Langlands-Weil conjectures, nonabelian class field theory |
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
Citations:
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