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

2024/07/15 by Roy Joshua⋆, Joshua, Roy, Pablo Pelaez +1
Mathematics · #14D23 #14L30 #19E08 #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2407.10394

openalex publication_date 2024/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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