Products and duality in Waldhausen categories

Weiss, Michael; Williams, Bruce

doi:10.1090/S0002-9947-99-02552-0

Products and duality in Waldhausen categories
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by Michael S. Weiss and Bruce Williams

Trans. Amer. Math. Soc. 352 (2000), 689-709

DOI: https://doi.org/10.1090/S0002-9947-99-02552-0

Published electronically: October 5, 1999

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Abstract:

The natural transformation $\Xi$ from $\mathbf {L}$–theory to the Tate cohomology of $\mathbb {Z} /2$ acting on $\mathbf {K}$–theory commutes with external products. Corollary: The Tate cohomology of $\mathbb {Z} /2$ acting on the $\mathbf {K}$–theory of any ring with involution is a generalized Eilenberg–Mac Lane spectrum, and it is 4–periodic.

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