Motivic cohomology of fat points in Milnor range via formal and rigid geometries

2021/08/31 by Jinhyun Park, Park, Jinhyun
Mathematics · #13F25 #14B20 #16W60 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Primary 14C25 #Secondary 19D45

paper · pdf · doi:10.48550/arxiv.2108.13563

openalex publication_date 2021/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a formal scheme based cycle model for the motivic cohomology of the fat points defined by the truncated polynomial rings k[t]/(t^m) with m ≥ 2, in one variable over a field k. We compute their Milnor range cycle class groups when the field has sufficiently many elements. With some aids from rigid analytic geometry and the Gersten conjecture for the Milnor K-theory resolved by M. Kerz, we prove that the resulting cycle class groups are isomorphic to the Milnor K-groups of the truncated polynomial rings, generalizing a theorem of Nesterenko-Suslin and Totaro.

Related

• Motivic cohomology of fat points in Milnor range
• Milnor K-theory of p-adic rings
• Motivic cohomology of twisted flag varieties
• Milnor excision for motivic spectra
• The Milnor-Witt motivic ring spectrum and its associated theories