Explicit determination of root numbers of abelian varieties
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- by Armand Brumer, Kenneth Kramer and Maria Sabitova PDF
- Trans. Amer. Math. Soc. 370 (2018), 2589-2604 Request permission
Abstract:
Let $A$ be an abelian variety over a nonarchimedean local field of definition $K$ and let $W(A)$ be the root number of $A$. Let $F$ be a Galois extension of $K$ over which $A$ has semistable reduction, allowing $F = K$. We analyze $W(A)$ in terms of contributions from the toric and abelian variety components of the closed fibers of the Néron models of $A$ over the ring of integers of $K$ and of $F$. In particular, our results can be used to calculate $W(A)$ in two main instances: first, for abelian varieties with additive reduction over $K$ and totally toroidal reduction over $F$, provided that the residue characteristic of $K$ is odd; second, for the Jacobian $A = J(C)$ of a stable curve $C$ over $K$.References
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Additional Information
- Armand Brumer
- Affiliation: Department of Mathematics, Fordham University, Bronx, New York 10458
- MR Author ID: 272178
- Email: brumer@fordham.edu
- Kenneth Kramer
- Affiliation: Department of Mathematics, Queens College, Flushing, New York 11367—and—The Graduate Center CUNY, New York, New York 10016
- MR Author ID: 194747
- Email: kkramer@qc.cuny.edu
- Maria Sabitova
- Affiliation: Department of Mathematics, Queens College, Flushing, New York 11367—and—The Graduate Center CUNY, New York, New York 10016
- MR Author ID: 707297
- Email: maria.sabitova@qc.cuny.edu
- Received by editor(s): March 19, 2015
- Received by editor(s) in revised form: February 3, 2016, and July 24, 2016
- Published electronically: December 26, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 2589-2604
- MSC (2010): Primary 11G10; Secondary 11G25, 11S20
- DOI: https://doi.org/10.1090/tran/7116
- MathSciNet review: 3748578