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Hidden structures on semistable curves. (English) Zbl 1251.11047
Berger, Laurent (ed.) et al., Représentations \(p\)-adiques de groupes \(p\)-adiques III: Méthodes globales et géométriques. Paris: Société Mathématique de France (ISBN 978-2-85629-282-2/pbk). Astérisque 331, 179-254 (2010).
Summary: Let \(V\) be the ring of integers of a finite extension of \(\mathbb Q_p\) and let \(X\) be a proper curve over \(V\) with semistable special fiber and smooth generic fiber. In this article we explicitly describe the Frobenius and monodromy operators on the log crystalline cohomology of \(X\) with values in a regular \(\log F\)-isocrystal in terms of \(p\)-adic integration. We have a version for open curves and as an application we prove that two differently defined \(\mathcal L\)-invariants, attached to a split multiplicative at \(p\) new elliptic eigenform, are equal.
For the entire collection see [Zbl 1192.11002].

MSC:
11G20 Curves over finite and local fields
11G25 Varieties over finite and local fields
11F11 Holomorphic modular forms of integral weight
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