2023/11/03 by Lünnemann, Maria
#13F35 #14A15 #14F10 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.02220
Let X be a smooth scheme over a finitely generated flat ℤ-, ℤ(p)- or ℤp-algebra R. Evaluated at finite truncation sets S, the relative de Rham-Witt complex WSΩX/R\bullet is a quotient of the de Rham complex Ω\bulletWS(X)/WS(R), which can be computed affine locally via explicit, but complicated relations. In this paper we prove that WSΩX/R\bullet is the torsionless quotient of the usual de Rham complex Ω\bulletWS(X)/WS(R) on the singular scheme WS(X). This result was suggested by comparison with a similar modification of the de Rham complex in the theory of singular varieties.