Vol. 2, No. 4, 2017

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Stable operations and cooperations in derived Witt theory with rational coefficients

Alexey Ananyevskiy

Vol. 2 (2017), No. 4, 517–560
Abstract

The algebras of stable operations and cooperations in derived Witt theory with rational coefficients are computed and an additive description of cooperations in derived Witt theory is given. The answer is parallel to the well-known case of K-theory of real vector bundles in topology. In particular, we show that stable operations in derived Witt theory with rational coefficients are given by the values on the powers of the Bott element.

Keywords
derived Witt groups, operations, cooperations
Mathematical Subject Classification 2010
Primary: 14F42, 14F99, 19G12
Milestones
Received: 14 November 2016
Revised: 10 February 2017
Accepted: 6 March 2017
Published: 18 July 2017
Authors
Alexey Ananyevskiy
Institute for Advanced Study
Princeton, NJ
United States
Chebyshev Laboratory
St. Petersburg State University
St. Petersburg
Russia