The Riemann-Roch Theorem on higher dimensional complex noncommutative tori

Published 24 Jul 2019 in math.OA, math.AG, and math.KT | (1907.10200v1)

Abstract: We 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.

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