Varghese, M.Rosenberg, J.2020-01-082020-01-082020Journal of Geometry and Physics, 2020; 147:103534-1-103534-90393-04401879-1662http://hdl.handle.net/2440/122600We prove analogues of the Riemann–Roch Theorem and the Hodge Theorem for noncommutative tori (of any dimension) equipped with complex structures, and discuss implications for the question of how to distinguish “noncommutative abelian varieties” from “non-algebraic” noncommutative complex tori.en© 2019 Elsevier B.V. All rights reserved.Noncommutative torus; Abelian variety; Index theory; Riemann–Roch Theorem; Hodge theoremJournal article100000525110.1016/j.geomphys.2019.1035340005014036000092-s2.0-85074323599502253Varghese, M. [0000-0002-1100-3595]