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A Lefschetz-Riemann-Roch theorem for singular schemes

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.