𝐴_{∞}-structures associated with pairs of 1-spherical objects and noncommutative orders over curves

Polishchuk, Alexander

doi:10.1090/tran/8140

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

Author: Alexander Polishchuk
Journal: Trans. Amer. Math. Soc. 373 (2020), 6029-6093
MSC (2010): Primary 14F05, 16E35
DOI: https://doi.org/10.1090/tran/8140
Published electronically: July 3, 2020
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Abstract: We show that pairs of -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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