Semistable abelian varieties and maximal torsion 1-crystalline submodules
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- Semistable abelian varieties and maximal torsion
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Let p be a prime, let K be a discretely valued extension of Qp, and let AK be an abelian K-variety with semistable reduction. Extending work by Kim and Marshall from the case where p > 2 and K/Qp is unramified, we prove an l = p complement of a Galois cohomological formula of Grothendieck for the l-primary part of the Néron component group of AK . Our proof in-volves constructing, for each m ∈ Z≥0, a finite flat OK-group scheme with generic fiber equal to the maximal 1-crystalline submodule of AK [pm ]. As a corollary, we have a new proof of the Coleman–Iovita monodromy criterion for good reduction of abelian K-varieties.
Original language | English |
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Journal | Journal de Theorie des Nombres de Bordeaux |
Volume | 33 |
Issue number | 1 |
Pages (from-to) | 39-81 |
Number of pages | 43 |
ISSN | 1246-7405 |
DOIs | |
Publication status | Published - 2021 |
Bibliographical note
Publisher Copyright:
© Société Arithmétique de Bordeaux, 2021, tous droits réservés.
- Log 1-motive, Néron component group, Torsion 1-crystalline representation
Research areas
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