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arXiv · 2609.32599

Riemann-Roch for 0-cycles on a singular variety

Marc Levine
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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 $X^*\subset X$ be a closed subset of dimension $<d$ such that $X\setminus X^*$ is regular of dimension $d$. Using a modification $\text{CH}^d(X, X^*)$ 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 $c_d:K_0(X)\to \text{CH}^d(X, X^*)$, a cycle class map from $\text{CH}^d(X, X^*)$ 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.

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Marc Levine. 2026-09-26. Riemann-Roch for 0-cycles on a singular variety. https://arxiv.org/abs/2609.32599

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