Relative K-theory via 0-cycles in finite characteristic

2019/10/15 by Gupta, Rahul, Krishna, Amalendu
#19E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14C25 #Secondary 19E08

paper · doi:10.48550/arxiv.1910.06630

Abstract

Let R be a regular semi-local ring, essentially of finite type over an infinite perfect field of characteristic p ≥ 3. We show that the cycle class map with modulus from an earlier work of the authors induces a pro-isomorphism between the additive higher Chow groups of relative 0-cycles and the relative K-theory of truncated polynomial rings over R. This settles the problem of equating 0-cycles with modulus and relative K-theory of such rings via the cycle class map.

Related

• Zero-cycles with modulus and relative K-theory
• A cycle class map from Chow groups with modulus to relative K-theory
• A local to global principle for higher zero-cycles
• Relative K-theory and class field theory for arithmetic surfaces
• Rigidity for relative 0-cycles