2006/12/07 by Lawrence Taylor, Taylor, Lawrence
Mathematics · #11U09 #54G15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Number Theory (math.NT) #math.LO #math.NT #msc:11U09 #msc:54G15
paper · pdf · doi:10.48550/arxiv.math/0612186
38 pages. Adapted from a chapter of the author's PhD thesis
openalex publication_date 2006/12/07 · arxiv created 2007/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of defining line bundles over certain non-Hausdorff spaces known as Quantum Tori, motivated by the proposed theory of Real Multiplication for real quadratic fields. We draw analogies from the theory of Line Bundles over Complex Tori to define a non-trivial cohomological notion of Line Bundles over Quantum Tori. We prove a structure theorem for isomorphism classes of such line bundles analogous to the Appel-Humbert Theorem for Complex Tori. In the second half of this text we consider Lines Bundles over Quantum Tori as topological spaces, and compare this notion with the cohomological definition. We define the Chern class of a line bundle and link this to an alternating pairing on a certain subgroup of Quantum Tori. Finally we investigate how our results are related to the study of Quantum Tori by Zilber using Model theoretic techniques.