Generalized Jacobians and explicit descents

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dc.contributor.authorCreutz B
dc.date.accessioned2021-09-29T22:04:33Z
dc.date.available2021-09-29T22:04:33Z
dc.date.issued2019en
dc.date.updated2019-10-15T20:59:48Z
dc.description.abstractWe develop a cohomological description of explicit descents in terms of generalized Jacobians, generalizing the known description for hyperelliptic curves. Specifically, given an integer n dividing the degree of some reduced, effective and base point free divisor m on a curve C, we show that multiplication by n on the generalized Jacobian Jm factors through an isogeny ϕ : Am --> Jm whose kernel is dual to the Galois module of divisor classes D such that nD is linearly equivalent to some multiple of m. By geometric class field theory, this corresponds to an abelian covering of Ck := C xSpec k Spec(k) of exponent n unramified outside m. We show that the n-coverings of C parameterized by explicit descents are the maximal unramified subcoverings of the k-forms of this ramified covering. We present applications to the computation of Mordell-Weil ranks of nonhyperelliptic curves.en
dc.identifier.citationCreutz B (2019). Generalized Jacobians and explicit descents. Mathematics of Computation. Mathematics of Computation. 1-1.en
dc.identifier.doihttps://doi.org/10.1090/mcom/3491
dc.identifier.issn0025-5718
dc.identifier.issn1088-6842
dc.identifier.urihttps://hdl.handle.net/10092/18000
dc.language.isoen
dc.publisherMathematics of Computationen
dc.subjectmath.NTen
dc.subject.anzsrcFields of Research::49 - Mathematical sciencesen
dc.titleGeneralized Jacobians and explicit descentsen
dc.typeDiscussion / Working Papersen
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