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\({\mathcal {L}}\) -invariants of p-adically uniformized varieties

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Abstract

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.

Résumé

Nous construisons deux types de L-invariants attachés aux variétés qui sont uniformisées par domaine symétrique padique de Drinfeld. Le premier est cohomologique, et le second analytique, selon une théorie de l’intégration p-adique. Nous conjecturons que les deux L-invariants coïncident, et discuterons des applications arithmétiques possibles.

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Notes

  1. See however the recent work of Chida et al. [9].

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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University, Beersheba, Israel

    Amnon Besser

  2. Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel

    Ehud de Shalit

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  1. Amnon Besser
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  2. Ehud de Shalit
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Correspondence to Ehud de Shalit.

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Besser, A., de Shalit, E. \({\mathcal {L}}\) -invariants of p-adically uniformized varieties. Ann. Math. Québec 40, 29–54 (2016). https://doi.org/10.1007/s40316-015-0047-1

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