Adelic descent for K-theory

2021/11/13 by Hyungseop Kim, Kim, Hyungseop · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.KT

paper · pdf · doi:10.48550/arxiv.2111.07202

19 pages, comments welcome

arxiv created 2021/11/13 · arxiv updated 2021/11/16

Abstract

We prove an adelic descent result for localizing invariants: for each Noetherian scheme X of finite Krull dimension and any localizing invariant E, e.g., algebraic K-theory of Bass-Thomason, there is an equivalence E(X)≃ lim E(A^⋅_red(X)), where A^⋅_red(X) denotes Beilinson's semi-cosimplicial ring of reduced adeles on X. We deduce the equivalence from a closely related cubical descent result, which we prove by establishing certain exact sequences of perfect module categories over adele rings.

Cited by

• Adelic descent for continuous localizing invariants

Related

• Adelic cohomology
• Higher Algebraic K-Theory of Schemes and of Derived Categories
• Adelic descent for continuous localizing invariants
• Beilinson-Parshin adeles via solid algebraic geometry
• Finite descent obstruction and non-abelian reciprocity