To a conical symplectic resolution with Hamiltonian torus action, Braden--Proudfoot--Licata--
Webster associate a category O, defined using deformation quantization (DQ) modules. It …

We provide a prorepresenting object for the noncommutative derived deformation problem
of deforming a module X over a differential graded algebra. Roughly, we show that the …

Let A be a commutative ring, and let a be a weakly proregular ideal in A.(If A is noetherian
then any ideal in it is weakly proregular.) Suppose M is a compact generator of the category …

A version of the Bondal-Orlov conjecture, proved by Bridgeland, states that if $ X $ and $ Y $
are smooth complex projective threefolds linked by a flop, then they are derived equivalent …

A result of André Weil allows one to describe rank-categories, we conclude that a
Noetherian scheme can be reconstructed from the co-simplicial ring of adèles. We view this …

We generalize the theory of Contou-Carr\ere symbols to higher dimensions. To an $(n+ 1) $-
tuple $ f_0,\dots, f_n\in A ((t_1))\cdots ((t_n))^{\times} $, where $ A $ denotes a commutative …

We show that Braun-Chuang-Lazarev's derived quotient prorepresents a naturally defined
noncommutative derived deformation functor. Given a noncommutative partial resolution of a …

We generalize Contou-Carrère symbols to higher dimensions. To an $(n+ 1) $-tuple $
f_0,\dots, f_n\in A ((t_1))\cdots ((t_n))^{\times} $, where $ A $ denotes an algebra over a field …

We show that a derived bi-duality dg-module is quasi-isomorphic to the homotopy limit of a
certain tautological functor. This is a simple observation, which seems to be true in wider …

Gabriel topology is a special class of linear topology on rings, which plays an important role
in the theory of localization of (not necessary commutative) rings []. Several evidences have …