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SUMMARY:Purity in tensor-triangular geometry - Jordan  Williamson (Charles
  University\, Prague)
DTSTART:20240528T083000Z
DTEND:20240528T093000Z
UID:TALK217201@talks.cam.ac.uk
DESCRIPTION:Tensor-triangular geometry provides a broad framework to study
  tensor-triangulated categories arising in nature. Just as any commutative
  ring has its Zariski spectrum\, any tensor-triangulated category has a sp
 ace called its Balmer spectrum which carries the universal support theory 
 classifying thick tensor ideals. There is also a closely related space cal
 led the homological spectrum from which one can recover the Balmer spectru
 m. Another space associated to any triangulated category is the Ziegler sp
 ectrum which contains all the data about the pure structure. I will explai
 n how the homological spectrum may be constructed from the Ziegler spectru
 m\, thus giving a bridge between tensor-triangular geometry and purity. I'
 ll explain an application of this to functoriality in tensor-triangular ge
 ometry. Time permitting\, I&rsquo\;ll explain how the ideas behind this al
 so may be applied in representation theory in the study of rank functions 
 and t-structures. This is based on joint work with Isaac Bird.
LOCATION:External
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