Arakelov theory of noncommutative arithmetic surfaces

2008/01/08 by Borek, Thomas
#14A22 (Secondary) #14G40 (Primary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0801.1225

Abstract

The purpose of this paper is to initiate Arakelov theory in a noncommutative setting. More precisely, we are concerned with noncommutative arithmetic surfaces. We introduce a version of arithmetic intersection theory on noncommutative arithmetic surfaces and we prove an arithmetic Riemann-Roch theorem in this setup.

Related

• Arakelov theory of noncommutative arithmetic curves
• Arakelov theory on arithmetic surfaces over a trivially valued field
• Quasi-projective and formal-analytic arithmetic surfaces
• Riemann-Hurwitz Formula for Arithmetic Surfaces
• An arithmetic Riemann-Roch theorem in higher degrees