Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Explicit determination of root numbers of abelian varieties
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 11G10, 11G25, 11S20
  • Retrieve articles in all journals with MSC (2010): 11G10, 11G25, 11S20
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