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arXiv · 2507.00221

Algebraic $K$-theory of coherent spaces

Georg Lehner
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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.

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Georg Lehner. 2025-06-30. Algebraic $K$-theory of coherent spaces. https://arxiv.org/abs/2507.00221

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