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arXiv · 1809.01981

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

Quan Xu
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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.

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Quan Xu. 2018-09-03. The Deligne pairing and a functorial Riemann Roch theorem in positive characteristic. https://arxiv.org/abs/1809.01981

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