Homotopy invariance of higher K-theory for abelian categories

2013/04/13 by Mochizuki, Satoshi, Sannai, Akiyoshi
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1304.3784

Abstract

The main theorem in this paper is that the base change functor from a noetherian abelian category to its noetherian polynomial category induces an isomorphism on K-theory. The main theorem implies the well-known fact that A¹-homotopy invariance of K'-theory for noetherian schemes.

Related

• Higher K-theory of polynomial categories
• A1-homotopy invariance of algebraic K-theory with coefficients and Kleinian singularities
• Motivic homotopy theory of group scheme actions
• A¹-homotopy invariance in spectral algebraic geometry
• Algebraic cobordism and a Conner-Floyd isomorphism for algebraic K-theory