On Deligne's functorial Riemann-Roch theorem in positive characteristic

Abstract

In this note, we give a proof for a variant of the functorial Deligne-Riemann-Roch theorem in positive characteristic based on ideas appearing in Pink and Rössler's proof of the Adams-Riemann-Roch theorem in positive characteristic (see [14]). The method of their proof appearing in [14], which is valid for any positive characteristic and which is completely different from the classical proof, will allow us to prove the functorial Deligne-Riemann-Roch theorem in a much easier and more direct way. Our proof is also partially compatible with Mumford's isomorphism.

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

“…However, its proof is usually not provided. I provide a complete proof by collecting all related known facts in the preprint (See [Qxu14]) (or see Thm15.7, [Kuz86]).…”