2024/06/24 by Nikolaev, Igor V.
#11M55 #14G40 #46L85 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2406.17063
We use K-theory of the C^*-algebras to study the Arakelov geometry, i.e. a compactification of the arithmetic schemes V→ Spec ~Z. In particular, it is proved that the Picard group of V is isomorphic to the K0-group of a Cuntz-Pimsner algebra associated to V. We apply the result to the finiteness problem for the algebraic varieties over number fields.