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- Title
GENERALIZED EXPLICIT DESCENT AND ITS APPLICATION TO CURVES OF GENUS 3.
- Authors
BRUIN, NILS; POONEN, BJORN; STOLL, MICHAEL
- 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 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.
- Subjects
STIMULUS generalization; ABELIAN varieties; ALGEBRAIC geometry; POLYNOMIALS; COEFFICIENTS (Statistics)
- Publication
Forum of Mathematics, Sigma, 2016, Vol 4, p1
- ISSN
2050-5094
- Publication type
Article
- DOI
10.1017/fms.2016.1