Abelian points on algebraic curves

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dc.creatorClark, Pete L.
dc.date2006-04-11
dc.date.accessioned2026-07-07T07:10:48Z
dc.date.available2026-07-07T07:10:48Z
dc.descriptionWe study the question of whether algebraic curves of a given genus g defined over a field K must have points rational over the maximal abelian extension K^{ab} of K. We give: (i) an explicit family of diagonal plane cubic curves with Q^{ab}-points, (ii) for every number field K, a genus one curve C_{/Q} with no K^{ab}-points, and (iii) for every g \geq 4 an algebraic curve C_{/Q} of genus g with no Q^{ab}-points. In an appendix, we discuss varieties over Q((t)), obtaining in particular a curve of genus 3 without (Q((t)))^{ab}-points.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0604263
dc.identifierhttp://arxiv.org/abs/math/0604263
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111534
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.titleAbelian points on algebraic curves
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