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Online: The dark side of the D(moon)

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Scott Balchin
Peter Teicher, Arunima Ray, Tobias Barthel
Mon, 2020-10-05 14:30 - 14:50
Parent event: 
MPIM Topology Seminar

Zoom Meeting ID: 916 5855 1117
For password see the email or contact: Arunima Ray or Tobias Barthel

Any abelian group can be reconstructed from its rationalized and p-completed parts. This object-wise decomposition can be lifted to several categorical decompositions of D(Z) -- the derived category of abelian groups. In fact, given any (suitably well-behaved) commutative ring R, a similar process can be performed where D(R) is decomposed using the data of its Zariski prime spectrum.

Derived categories of rings form a class of examples of tensor-triangulated categories. In this talk I will discuss ways of splitting tt-categories by shining them through a prism. These prisms are constructed using a suitable generalization of the Zariski prime spectrum of a ring, and the splitting is achieved by using compatible notions of localization and completion.
The goal is to use this machinery to better understand the category of rational-valued equivariant cohomology theories for compact Lie groups, and eventually to aid in building algebraic models for such.
[j/w Tobias Barthel and J.P.C.Greenlees]



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