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SUMMARY:Polynomial functors and algebraic K-theory - Akhil Mathew (Harvard
  University\; Clay Mathematics Institute)
DTSTART:20170329T080000Z
DTEND:20170329T090000Z
UID:TALK71690@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The Grothendieck group K_0 of a commutative ring is well-known
  to be a &lambda\;-ring: although the exterior powers are non-additive\, t
 hey induce maps on K_0 satisfying various universal identities. The &lambd
 a\;-operations yield homomorphisms on higher K-groups.   In joint work in 
 progress with  Glasman and Nikolaus\, we give a  general framework for suc
 h operations. Namely\, we show that the  K-theory space is naturally funct
 orial for polynomial functors\, and  describe a universal property of the 
 extended K-theory functor. This  extends an earlier algebraic result of Do
 ld for K_0. In this picture\, the &lambda\;-operations come from the stric
 t polynomial functors of Friedlander-Suslin. <br>
LOCATION:Seminar Room 1\, Newton Institute
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