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

Abstract

We show that pairs $(X,Y)$ of 1-spherical objects in $A_{\infty }$-categories, such that the morphism space $\mathrm{Hom}(X,Y)$ 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 $\mathbb{Z}$.

v1: 62 pages, v2: 67 pages

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• Grothendieck Duality for Deligne-Mumford Stacks
• Arithmetic mirror symmetry for the 2-torus
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Cited by in corpus (1)

• Elliptic bihamiltonian structures from relative shifted Poisson structures