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$\lambda$-ring structures
on the $K$-theory of algebraic stacks
Roy Joshua and Pablo Pelaez |
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Vol. 9 (2024), No. 3, 519–581
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Abstract |
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We consider the -theory of smooth algebraic stacks, establish and operations, and show that the higher -theory of such stacks is always a pre--ring, and is a -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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Keywords
algebraic stacks, $K$-theory, lambda operations
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Mathematical Subject Classification
Primary: 14C35, 14D23, 19E08
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Milestones
Received: 3 September 2023
Revised: 15 April 2024
Accepted: 14 July 2024
Published: 1 October 2024
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Authors |
| Roy Joshua | |
| Department of Mathematics Ohio State University Columbus, OH United States |
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| Pablo Pelaez | |
| Instituto de Matemáticas IMATE, UNAM Ciudad Universitaria Ciudad de México Mexico |
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| © 2024 MSP (Mathematical Sciences Publishers). |
