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Seminar

AT Research Seminar: Global algebraic K-theory March 06, 2014 (01:30 PM PST - 02:30 PM PST)
Parent Program: Algebraic Topology
Location: MSRI: Simons Auditorium
Speaker(s) Stefan Schwede (Universit├Ąt Bonn)
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Given a commutative ring R, I will introduce a commutative symmetric ring spectrum K_gl R, the `global algebraic K-theory' of R. Its underlying non-equivariant homotopy type is that of the algebraic K-theory spectrum, and its G-fixed point spectrum, for a finite group G, is the K-theory spectrum of finitely generated RG-modules which are R-projective.

 

The construction is a special case of a `global delooping machine' that is remeniscent of G-equivariant deloopings obtained from the Segal-Shimakawa approach based on G-Gamma categories. The central roles is played by a certain categorical operad that behaves like a discrete linear isometries operad.

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