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Finite Weil restriction of curves

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Flynn, Victor and Testa, Damiano (2015) Finite Weil restriction of curves. Monatshefte fur Mathematik, 176 (2). pp. 197-218. doi:10.1007/s00605-014-0711-6 ISSN 0026-9255.

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Official URL: https://doi.org/10.1007/s00605-014-0711-6

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Abstract

Given number fields L⊃K, smooth projective curves C defined over L and B defined over K, and a non-constant L-morphism h:C→B_L,we consider the curve C_h defined over K whose K-rational points parametrize the L-rational points on C whose images under h are defined over K. Our construction provides a framework which includes as a special case that used in Elliptic Curve Chabauty techniques and their higher genus versions. The set C_h(K) can be infinite only when C has genus at most 1; we analyze completely the case when C has genus 1.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Curves, Algebraic, Jacobians, Weil conjectures
Journal or Publication Title: Monatshefte fur Mathematik
Publisher: Springer Vienna
ISSN: 0026-9255
Official Date: February 2015
Dates:
DateEvent
February 2015Published
3 December 2014Available
10 November 2014Accepted
Volume: 176
Number: 2
Page Range: pp. 197-218
DOI: 10.1007/s00605-014-0711-6
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 13 July 2018
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/F060661/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/K019279/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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