A module structure and a vanishing theorem for cycles with modulus

2014/12/23 by Krishna, Amalendu, Park, Jinhyun
#13F35 (Secondary) #14C25 (Primary) #19E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1412.7396

Abstract

We show that the higher Chow groups with modulus of Binda-Kerz-Saito for a smooth quasi-projective scheme X is a module over the Chow ring of X. From this, we deduce certain pull-backs, the projective bundle formula, and the blow-up formula for higher Chow groups with modulus. We prove vanishing of 0-cycles of higher Chow groups with modulus on various affine varieties of dimension at least two. This shows in particular that the multivariate analogue of Bloch-Esnault--Rülling computations of additive higher Chow groups of 0-cycles vanishes.

Related

• A moving lemma for cycles with very ample modulus
• A decomposition theorem for 0-cycles and applications
• Cycle class maps for Chow groups of zero-cycles with modulus
• Arithmetic Cycles with Modulus
• Additive Chow groups of schemes