Fourier--Mukai transforms for non-commutative complex tori

2023/01/10 by Nobuki Okuda, Okuda, Nobuki
Mathematics · Physics and Astronomy · #14A22 #16S38 #18G80 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2301.03745

openalex publication_date 2023/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a complex torus of dimension g and X be the dual torus. For any g(g-1)/2-tuple λ of complex numbers of absolute value 1, we define a non-commutative complex torus X_λ as a sheaf of algebras on a real torus of dimension g. We prove that if all components of λ are roots of unity, then the category of coherent sheaves on X_λ is abelian and derived-equivalent to the category of coherent sheaves on X twisted by an element of the Brauer group of X determined by λ.

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