\({\mathcal{L}}\)-invariants of \(p\)-adically uniformized varieties. (English. French summary) Zbl 1375.14074
Summary: We construct two types of \({\mathcal{L}}\)-invariants attached to varieties which are uniformized by Drinfeld’s \(p\)-adic symmetric domain. The first is cohomological, and the second analytic, depending on a theory of \(p\)-adic integration. We conjecture that the two \({\mathcal{L}}\)-invariants coincide, and discuss possible arithmetic applications.
MSC:
| 14F30 | \(p\)-adic cohomology, crystalline cohomology |
| 14G22 | Rigid analytic geometry |
| 11G40 | \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture |
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