Kavli Affiliate: Yukinobu Toda | First 5 Authors: Yukinobu Toda, , , , | Summary: We show the existence of semiorthogonal decompositions of Donaldson-Thomas categories for $(-1)$-shifted cotangent derived stacks associated with $Theta$-stratifications on them. Our main result gives an analogue of window theorem for categorical DT theory, which has applications to d-critical analogue of […]

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 […]