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SUMMARY:An arithmetic refinement of homological mirror symmetry for the 2-
 torus -  Yanki Lekili  (Cambridge) 
DTSTART:20130207T140000Z
DTEND:20130207T150000Z
UID:TALK43229@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:We explore a refinement of homological mirror symmetry which r
 elates exact\nsymplectic topology to arithmetic algebraic geometry. We est
 ablish a derived\nequivalence of the Fukaya category of the 2- torus\, rel
 ative to a basepoint\,\nwith the category of perfect complexes on the Tate
  curve over Z[[q]]. It\nspecializes to an equivalence\, over Z\, of the Fu
 kaya category of the punctured\ntorus with perfect complexes on the nodal 
 Weierstrass curve y^2+xy=x^3\, and\,\nover the punctured disc Z((q))\, to 
 an integral refinement of the known\nstatement of homological mirror symme
 try for the 2- torus. We will survey a\ngeneral strategy of proof of homol
 ogical mirror symmetry while carrying it out\nin the specific case of the 
 2-torus. In contrast to the abstract statement of\nour main result\, the f
 ocus of the talk will be a concrete computation which we\nwill express in 
 more familiar terms. This is my joint work with Tim Perutz.
LOCATION:CMS\, MR4
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