2005/06/24 by Kurano, Kazuhiko
#13D40 #14C40 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.math/0506492
In the paper, by the singular Riemann-Roch theorem, it is proved that the class of the e-th Frobenius power can be described using the class of the canonical module for a normal local ring of positive characteristic. As a corollary, we prove that the coefficient of the second term of the Hilbert-Kunz function of a finitely generated A-module M vanishes if A is a Q-Gorenstein ring and M is of finite projective dimension. For a normal algebraic variety X over a perfect field of positive characteristic, it is proved that the first Chern class of the direct image of the structure sheaf via e-th Frobenius power can be described using the canonical divisor of X.