A Lefschetz-Riemann-Roch theorem for singular schemes

TL;DR

This paper extends the Lefschetz-Riemann-Roch theorem to singular projective schemes with diagonalisable group actions, broadening its applicability beyond previous results for singular varieties.

Contribution

It generalizes the Lefschetz-Riemann-Roch theorem to singular schemes with group actions, expanding the theoretical framework for algebraic geometry.

Findings

Proves a Lefschetz-Riemann-Roch theorem for singular schemes with group actions

Generalizes previous results from varieties to schemes

Applicable to schemes with diagonalisable group scheme actions

Abstract

In this paper, we prove a Lefschetz-Riemann-Roch theorem for singular projective schemes which admit diagonalisable group scheme actions, this result generalizes P. Baum, W. Fulton and G. Quart's Lefschetz-Riemann-Roch theorem for singular varieties (cf. \cite{BFQ}) to general scheme case.