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Mixed graded structures for the K-theory of Azumaya algebras

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KAH - K-theory, algebraic cycles and motivic homotopy theory

If we encode Morita theory for R-algebras as a monoidal category where morphisms are bimodules, then algebraic K-theory becomes a (lax) monoidal functor from this category to graded abelian groups. We show that if we restrict to Azumaya algebras, strong symmetry properties coming from the Goldman element allow to coherently lift certain Brauer subgroups to the the level of Morita equivalences, which gives rise to (graded-)commutative algebras of K-theory, graded over the corresponding Brauer subgroup. We also study analogue constructions for hermitian K-theory of Azumaya algebras with involution

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

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