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Thirteenth Algorithmic Number Theory Symposium ANTS-XIII
University of Wisconsin, Madison
July 16 – 20, 2018

Thirteenth Algorithmic Number Theory Symposium (ANTS-XIII)
July 16 – 20, 2018

Numerical computation of endomorphism rings of Jacobians

Nils Bruin, Jeroen Sijsling and Alexandre Zotine

Abstract: We give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as well as the decomposition of their Jacobians up to isogeny, can be calculated heuristically. Particular applications include the determination of (generically) non-Galois morphisms between curves and the identication of Prym varieties.

Files available: paper (PDF)     slides

© 2017-2018 Jennifer Paulhus (with thanks to Kiran S. Kedlaya, and by extension Pierrick Gaudry and Emmanuel Thomé)