The comparison of the 0-th Suslin homology and Chow groups of 0-cycles with modulus

TL;DR

This paper proves an isomorphism between Chow groups of zero cycles with modulus and 0-th Suslin homology for certain algebraic varieties, extending known results to higher dimensions and specific conditions.

Contribution

It establishes a new equivalence between Chow groups with modulus and Suslin homology for projective schemes with divisors, generalizing previous results.

Findings

Chow groups with modulus coincide with 0-th Suslin homology under specified conditions

The isomorphism holds for projective smooth schemes of any dimension

Results apply to surfaces over perfect fields of positive characteristic

Abstract

We show that, for a $K_0$-regular projective normal surface $X$ over a perfect field $k$ of positive characteristic and a reduced effective Cartier divisor $D\hookrightarrow X$, the Chow group of zero cycles on $X$ with modulus $D$ coincides with the 0-th Suslin homology of $X\setminus D$. Moreover, we show that this isomorphism also holds for a projective smooth scheme of any dimension with a reduced effective Cartier divisor.