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SUMMARY:Reflexivity and Hochschild Cohomology  - Isambard Goodbody (Unive
 rsity of Glasgow)
DTSTART:20240610T133000Z
DTEND:20240610T140000Z
UID:TALK217768@talks.cam.ac.uk
DESCRIPTION:Smooth and proper DG-categories are noncommutative versions of
  smooth and proper schemes which also include finite dimensional algebras 
 of finite global dimension. Kuznetsov and Shinder defined reflexive DG-cat
 egories as a generalisation\; they include all projective schemes and all 
 finite dimensional algebras.&nbsp\; Smooth and proper DG-categories can be
  characterised as the dualizable objects in the monoidal category of DG-ca
 tegories localised at Morita equivalences. The main result I&rsquo\;ll tal
 k about is a monoidal characterisation of reflexive DG-categories. This pr
 ovides a conceptual explanation for why there is some common information b
 etween D^b(mod A) and D^perf(A) for a finite dimensional algebra A and bet
 ween D^b(coh X) and D^perf(X) for a projective scheme X. One can use this 
 approach to prove that the Hochschild cohomology of a reflexive DG-categor
 y is isomorphic to that of its derived category of cohomologically finite 
 modules.
LOCATION:External
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