PreprintCC BY 4.0arXiv
Riemann-Roch for 0-cycles on a singular variety
Abstract
Let X be a quasi-projective scheme of dimension d over an infinite field k, such that X is reduced after removing all components of dimension <d, and let X*⊂ X be a closed subset of dimension <d such that X∖ X* is regular of dimension d. Using a modification CHd(X, X*) of the Chow group of 0-cycles on a singular variety defined by C. Weibel and the author in 1985, we construct a Chern class map cd:K0(X)→ CHd(X, X*), a cycle class map from CHd(X, X*) onto a subgroup FdK0(X) of K0(X), and prove a Riemann-Roch theorem computing the two compositions of these two maps.
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BibTeX
@misc{levine2026riemannroch,
title = {{Riemann-Roch for 0-cycles on a singular variety}},
author = {Marc Levine},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32599},
eprint = {2609.32599},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32599},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Riemann-Roch for 0-cycles on a singular variety
AU - Marc Levine
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32599
UR - https://arxiv.org/abs/2609.32599
AB - Let X be a quasi-projective scheme of dimension d over an infinite field k, such that X is reduced after removing all components of dimension <d, and let X^*⊂ X be a closed subset of dimension <d such that X∖ X^* is regular of dimension d. Using a modification CH^d(X, X^*) of the Chow group of 0-cycles on a singular variety defined by C. Weibel and the author in 1985, we construct a Chern class map c_d:K_0(X)→ CH^d(X, X^*), a cycle class map from CH^d(X, X^*) onto a subgroup F^dK_0(X) of K_0(X), and prove a Riemann-Roch theorem computing the two compositions of these two maps.
ER -