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arXiv · 2106.05493

Categorical Donaldson-Thomas theory for local surfaces: $\mathbb{Z}/2$-periodic version

Yukinobu Toda
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Abstract

We prove two kinds of $\mathbb{Z}/2$-periodic Koszul duality equivalences for triangulated categories of matrix factorizations associated with $(-1)$-shifted cotangents over quasi-smooth affine derived schemes. We use this result to define $\mathbb{Z}/2$-periodic version of Donaldson-Thomas categories for local surfaces, whose $\mathbb{C}^{\ast}$-equivariant version was introduced and developed in the author's previous paper. We compare $\mathbb{Z}/2$-periodic DT category with the $\mathbb{C}^{\ast}$-equivariant one, and deduce wall-crossing equivalences of $\mathbb{Z}/2$-periodic DT categories from those of $\mathbb{C}^{\ast}$-equivariant DT categories.

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Yukinobu Toda. 2021-06-10. Categorical Donaldson-Thomas theory for local surfaces: $\mathbb{Z}/2$-periodic version. https://arxiv.org/abs/2106.05493

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