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SUMMARY:Explicit Chabauty over Number Fields - Samir Siksek (Warwick)
DTSTART:20100302T143000Z
DTEND:20100302T153000Z
UID:TALK23199@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:Let _C_ be a curve of genus at least 2 over a number field _K_
  of degree _d_. Let _J_ be the Jacobian of _C_ and _r_ the rank of the Mor
 dell-Weil group _J(K)_. Chabauty is a practical method for explicitly comp
 uting _C(K)_ provided _r <= g - 1_. In unpublished work\, Wetherell sugges
 ted that Chabauty's method should still be applicable provided the weaker 
 bound _r <= d (g - 1)_ is satisfied. We give details of this and use it to
  solve the Diophantine equation _x^2^_ + _y^3^_ = _z^10^_ by reducing the 
 problem to determining the _K_-rational points on several genus 2 curves o
 ver _K_ = *Q*(cube root of 2).
LOCATION:MR13
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