On the Adams-Riemann-Roch theorem in positive characteristic. [With an appendix by B. Koeck: Another formula for the Bott element]

Abstract

We give a new proof of the Adams-Riemann-Roch theorem for a smooth projective morphism X ? Y, in the situation where Y is a scheme of characteristic p > 0, which is of finite type over a noetherian ring and carries an ample line bundle. This theorem implies the Hirzebruch-Riemann-Roch theorem in characteristic 0. We also answer a question of B. Koeck.[Appendix: The object of the appendix is to give another formula for the Bott element of a smooth morphism. This formula is analogous to a formula in the main part of the paper and extends a list of miraculous analogies explained in an earlier paper.