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Hermitian K-theory and trace methods

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Emanuele Dotto
University of Bonn
Thu, 15/12/2016 - 13:45 - 14:45
MPIM Lecture Hall

The Hermitian K-theory of a ring with anti-involution is the group-completion of its space of Hermitian forms and isometries. In recent work Hesselholt and Madsen describe this space as the $\mathbb{Z}/2$-fixed-points of an involution on the algebraic K-theory spectrum of the underlying ring. The geometric fixed-points of this $\mathbb{Z}/2$-spectrum are equivalent, at least when 2 is invertible, to the symmetric L-theory spectrum of the ring. I will discuss ongoing work on Hermitian and L-theoretical versions of topological Hochschild homology and on the corresponding trace map from Hermitian K-theory.

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