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Generalized explicit descent and its application to curves of genus 3

Title data

Bruin, Nils ; Poonen, Bjorn ; Stoll, Michael:
Generalized explicit descent and its application to curves of genus 3.
In: Forum of Mathematics, Sigma. Vol. 4 (2016) . - e6. - 80 pp..
ISSN 2050-5094
DOI: https://doi.org/10.1017/fms.2016.1

Project information

Project financing: Deutsche Forschungsgemeinschaft
Natural Sciences and Engineering Research Council
Guggenheim Foundation
Simons Foundation #340694
National Science Foundation grants DMS-0301280, DMS-0841321, and DMS-1069236

Abstract in another language

We introduce a common generalization of essentially all known methods for explicit computation of Selmer groups, which are used to bound the ranks of abelian varieties over global fields. We also simplify and extend the proofs relating what is computed to the cohomologically defined Selmer groups. Selmer group computations have been practical for many Jacobians of curves over ℚ of genus up to 2 since the 1990s, but our approach is the first to be practical for general curves of genus 3. We show that our approach succeeds on some genus 3 examples defined by polynomials with small coefficients.

Further data

Item Type: Article in a journal
Refereed: Yes
Subject classification: 2010 Mathematics Subject Classification: 11G30 (11G10 14G25 14H45)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 21 Jun 2016 07:45
Last Modified: 24 Oct 2017 14:16
URI: https://eref.uni-bayreuth.de/id/eprint/32844