Kavli Affiliate: Yukinobu Toda
| First 5 Authors: Yukinobu Toda, , , ,
| Summary:
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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