The Deligne pairing and a functorial Riemann Roch theorem in positive characteristic

Abstract

In this paper, we prove the functorial Riemann-Roch theorem in positive characteristic for a smooth and projective morphism with any relative dimension. In the case of relative dimension $1$, we have given an analogue with Deligne's functorial Riemann Roch theorem in previous author's paper. For any relative dimension, our result can deduce an analogue to the Knudsen-Mumford extension. The present result is a generalization, which mainly originated from the extended Deligne pairing by S. Zhang and the Adams Riemann Roch theorem in positive characteristic by R. Pink and D. Rössler.

arXiv commentThe functorial Riemann Roch theorem in positive characteristic has been proved for projective and smooth morphism of relative dimension $1$. Now, we extend the relative dimension $1$ to any relative dimension. The present paper is a generalization and can deduce an Knudsen-Mumford extension, somehow different from its original version of the extension. arXiv admin note: substantial text overlap with arXiv:1405.6063; text overlap with arXiv:0812.0254 by other authors