Abstract
AbstractWe prove a moving lemma that implies the contravariance of Bloch–Esnault’s additive higher Chow group in smooth affine schemes and that of Binda–Saito’s higher Chow group (taken in the Nisnevich topology).
Highlights
The current development was initiated by Bloch and Esnault [BE03] who introduced the additive higher Chow group TCH∗(X, n; m), and it has been a fruitful subject over the last decade
It is defined as the homology groups of the cycle complex with modulus zi(X|D, ). It contains all the groups above as particular cases. It is expected as a cycle-theoretic cohomology theory corresponding to the relative K-theory Kn(X, D)
In spite of being a candidate of a nice cohomology theory, it had been unknown if the additive higher Chow group and the higher Chow group with modulus are contravariant for arbitrary morphisms of smooth schemes
Summary
We recall Binda-Saito’s cycle complex, and the notion of constructible subsets and functions on noetherian topological spaces. After that we define certain subcomplexes of the cycle complex determined by data of constructible subsets of the variety
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
