GENERALIZED EXPLICIT DESCENT AND ITS APPLICATION TO CURVES OF GENUS 3
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960.17 KB
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Author(s)
Bruin, Nils
Stoll, Michael
Poonen, Bjorn
Date Issued
February 2016
Journal
Forum of Mathematics, Sigma
Publisher
Cambridge University Press (CUP)
Citation
BRUIN, NILS et al. “GENERALIZED EXPLICIT DESCENT AND ITS APPLICATION TO CURVES OF GENUS 3.” Forum of Mathematics, Sigma 4 (February 2016): e6 © 2016 The Author(s)
Version
Final published version
Abstract
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 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International License
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DOI of Published Version
https://doi.org/10.1017/FMS.2016.1
