Arithmetic quantum local systems over the moduli of curves

2025/01/16 by Gyujin Oh, Oh, Gyujin
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Quantum Computing Algorithms and Architecture #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2501.09377

openalex publication_date 2025/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an arithmetic analogue of the quantum local systems on the moduli of curves, and study its basic structure. Such an arithmetic local system gives rise to a uniform way of assigning a Galois cohomology class of the first geometric étale cohomology of a smooth proper curve over a number field.

Related

• On the quantum cohomology of the plane, old and new
• Algebraic cycles and local quantum cohomology
• Quantum arithmetic
• The local Gromov-Witten theory of curves
• Explicit computation of Galois representations occurring in families of curves