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SUMMARY:The Tambara Affine Line - Ben Spitz (University of Virginia)
DTSTART:20250429T143000Z
DTEND:20250429T153000Z
UID:TALK230368@talks.cam.ac.uk
DESCRIPTION:In equivariant stable homotopy theory\, objects called "Tambar
 a functors" play the role of commutative rings. Tambara functors are abstr
 act algebraic objects: they consist of sets with certain operations satisf
 ying certain axioms\; however\, the theory of Tambara functors is much les
 s developed than the theory of commutative rings\, in part because it is n
 ot clear exactly how to define the "Tambara analogs" of many classical not
 ions. Nonetheless\, we expect that Tambara functors admit a theory of comm
 utative algebra and algebraic geometry\, akin to the story for ordinary co
 mmutative rings. In this talk\, I will discuss recent progress in developi
 ng such a theory for Tambara functors &ndash\; in particular\, we prove a 
 version of the going-up theorem\, which allows for the first computation o
 f the "affine line" in Tambara algebraic geometry. This is joint work with
  David Chan\, David Mehrle\, J.D. Quigley\, and Danika Van Niel.
LOCATION:Seminar Room 2\, Newton Institute
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