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SUMMARY:Grigory Garkusha (Swansea)
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260423T052808Z
UID:OATS/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OATS/20/">Mo
 tivic Gamma-spaces</a>\nby Grigory Garkusha (Swansea) as part of Online al
 gebraic topology seminar\n\n\nAbstract\nThis is a joint work with Ivan Pan
 in and Paul Arne Østvær. We combine several mini miracles to achieve an 
 elementary understanding of infinite loop spaces and very effective spectr
 a in the algebro-geometric setting of motivic homotopy theory. Our approac
 h combines Gamma-spaces and framed correspondences into the concept of mot
 ivic Gamma-spaces\; these are continuous or enriched functors of two varia
 bles that take values in motivic spaces and are equipped with a framing. W
 e craft proofs of our main results by imposing further axioms on motivic G
 amma-spaces such as a Segal condition for simplicial Nisnevich sheaves\, c
 ancellation\, A1- and sigma-invariance\, Nisnevich excision\, Suslin contr
 actibility\, and grouplikeness. This adds to the discussion in the literat
 ure on coexisting points of view on the A1-homotopy theory of algebraic va
 rieties. As prime examples we discuss the motivic sphere spectrum\, algebr
 aic cobordism\, motivic cohomology\, and Milnor-Witt motivic cohomology.\n
LOCATION:https://researchseminars.org/talk/OATS/20/
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