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Polynomial functors and algebraic K-theory

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OASW02 - Subfactors, higher geometry, higher twists and almost Calabi-Yau algebras

The Grothendieck group K_0 of a commutative ring is well-known to be a λ-ring: although the exterior powers are non-additive, they induce maps on K_0 satisfying various universal identities. The λ-operations yield homomorphisms on higher K-groups. In joint work in progress with Glasman and Nikolaus, we give a general framework for such operations. Namely, we show that the K-theory space is naturally functorial for polynomial functors, and describe a universal property of the extended K-theory functor. This extends an earlier algebraic result of Dold for K_0. In this picture, the λ-operations come from the strict polynomial functors of Friedlander-Suslin.

This talk is part of the Isaac Newton Institute Seminar Series series.

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