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SUMMARY:A constructive approach to geometric algebra - Achilleas Kryftis\,
  DPMMS
DTSTART:20130521T131500Z
DTEND:20130521T141500Z
UID:TALK44712@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:In classical geometric algebra\, we prove that the synthetic a
 nd the projective approaches to the affine and projective planes are equiv
 alent. This classical approach is not entirely constructive and it is base
 d on fields.\n\nWe will present a constructive version of this based on lo
 cal rings: we will define what are the projective and affine planes over a
  given local ring (in a topos)\, and we will give the geometric theories o
 f projective and affine planes satisfied by these constructions. Moreover\
 , we will show how to construct a local ring given a model of that theory.
  These constructions induce geometric morphisms between the classifying to
 poses of the theories of affine and projective planes\, and the theory of 
 local rings.
LOCATION:MR5\, Centre for Mathematical Sciences
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