Lambda-ring structures on the K-theory of algebraic stacks
In this paper we consider the K-theory of smooth algebraic stacks, establish lambda and gamma operations, and show that the higher K-theory of such stacks is always a pre-lambda-ring, and is a lambda-ring if every coherent sheaf is the quotient of a vector bundle. As a consequence, we are able to de...
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Zusammenfassung: | In this paper we consider the K-theory of smooth algebraic stacks, establish
lambda and gamma operations, and show that the higher K-theory of such stacks
is always a pre-lambda-ring, and is a lambda-ring if every coherent sheaf is
the quotient of a vector bundle. As a consequence, we are able to define Adams
operations and absolute cohomology for smooth algebraic stacks satisfying this
hypothesis. We also obtain a comparison of the absolute cohomology with the
equivariant higher Chow groups in certain special cases. |
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DOI: | 10.48550/arxiv.2407.10394 |