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Transactions of the American Mathematical Society

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$ A_\infty$-structures associated with pairs of $ 1$-spherical objects and noncommutative orders over curves

Author: Alexander Polishchuk
Journal: Trans. Amer. Math. Soc. 373 (2020), 6029-6093
MSC (2010): Primary 14F05, 16E35
Published electronically: July 3, 2020
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Abstract: We show that pairs $ (X,Y)$ of $ 1$-spherical objects in $ A_\infty $-categories, such that the morphism space $ \operatorname {Hom}(X,Y)$ is concentrated in degree 0, can be described by certain noncommutative orders over (possibly stacky) curves. In fact, we establish a more precise correspondence at the level of isomorphism of moduli spaces which we show to be affine schemes of finite type over $ {\Bbb Z}$.

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Alexander Polishchuk
Affiliation: University of Oregon, Eugene, Oregon 97403; National Research University Higher School of Economics, Moscow, Russian Federation; and Korea Institute for Advanced Study, Seoul, South Korea
MR Author ID: 339630

Received by editor(s): June 16, 2018
Received by editor(s) in revised form: September 27, 2019
Published electronically: July 3, 2020
Additional Notes: The author was supported in part by the NSF grant DMS-1700642, by the National Center of Competence in Research “SwissMAP — The Mathematics of Physics” of the Swiss National Science Foundation, and within the framework of the HSE University Basic Research Program, and by the Russian Academic Excellence Project ‘5-100’.
Article copyright: © Copyright 2020 American Mathematical Society