Quantum arithmetic of Drinfeld modules

2025/09/01 by Nikolaev, Igor V.
#11M55 #46L85 #FOS: Mathematics #Number Theory (math.NT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2509.01818

Abstract

We study quantum invariants of projective varieties over number fields. Namely, an explicit formula for a functor \mathscrQ on such varieties is proved. The case of abelian varieties with complex multiplication is treated in detail.

Citations

• Non-abelian class field theory and higher dimensional noncommutative tori
• Noncommutative curves and noncommutative surfaces

Related

• Quantum arithmetic
• Quantum Drinfeld Modules I: Quantum Modular Invariant and Hilbert Class Fields
• The quantum D-module of product varieties
• Varieties of modules over the quantum plane
• Counting on the variety of modules over the quantum plane