Algebraic K-theory of coherent spaces

2025/06/30 by Lehner, Georg
#18F20 #54B40 #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #K-Theory and Homology (math.KT) #Primary: 19D99 #Secondary: 06D22

paper · doi:10.48550/arxiv.2507.00221

Abstract

We give a description of the value of a finitary localizing invariant, such as algebraic K-theory, on the category of sheaves on a locally coherent space X. This in particular includes all spaces that arise as spectra of commutative rings. As applications we discuss the connection between scissors congruence K-theory and Topological Hochschild Homology of certain locally coherent spaces, as well as the algebraic K-theory of a measure space.

Citations

• The animation of the opposite of finite sets
• Hypersheaves and bases
• Scissors automorphism groups and their homology
• K-theory and localizing invariants of large categories
• On higher scissors congruence
• Higher Lawvere theories
• Scissors Congruence as K-theory
• Symmetric spectra

Related

• Relative Tate Objects and Boundary Maps in the K-Theory of Coherent\n Sheaves
• A remark on Continuous K-theory and Fourier-Sato transform
• K-theory and localizing invariants of large categories
• A representation for algebraic K-theory of quasi-coherent modules over affine spectral schemes
• K-homology in algebraic geometry and D-branes