A Riemann–Roch theorem

Abstract

In this paper, we prove an analogue of this theorem for weak Euler classes. Weak Euler classes take values in weak Euler class groups. The definitions of the weak Euler class group and weak Euler classes were achieved by relaxing the definitions of the Euler class group and Euler classes. The original definitions of the Euler class group and the Euler classes, for smooth affine algebras over fields, were given by M.V. Nori. For background literature we refer to [1,2,8,11,12,15]. For noetherian commutative rings A, with dimA = n 2 and a line bundle L on Spec(A), the weak Euler class group E0(A,L) has been defined in [2] as the quotient