Lambda-ring structures on the K-theory of algebraic stacks

Fuente: arXiv
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Main Authors: Joshua, Roy, Pelaez, Pablo
Format: Preprint
Published: 2024
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author Joshua, Roy
Pelaez, Pablo
author_facet Joshua, Roy
Pelaez, Pablo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_10394
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Lambda-ring structures on the K-theory of algebraic stacks
Joshua, Roy
Pelaez, Pablo
K-Theory and Homology
19E08, 14D23, 14L30
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.
title Lambda-ring structures on the K-theory of algebraic stacks
topic K-Theory and Homology
19E08, 14D23, 14L30
url https://arxiv.org/abs/2407.10394