Dimitrov, George Katzarkov, Ludmil
Published in
Selecta Mathematica

In this paper we introduce new categorical notions and give many examples. In an earlier paper we proved that the Bridgeland stability space on the derived category of representations of K(l), the l-Kronecker quiver, is biholomorphic to C×H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amss...

Rizzardo, Alice Van den Bergh, Michel Neeman, Amnon
Published in
Inventiones mathematicae

Orlov’s famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier–Mukai functor. In this paper we show that this result is false without the fully faithfulness hypothesis. We also show that our functor does not lift to the homo...

Chen, Jian Min Lin, Ya Nan Ruan, Shi Quan
Published in
Acta Mathematica Sinica, English Series

The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting objects with tubular endomorphism algebras for the case of genus one via cluster tilting theory.

Wang, Xin Shen, Yuan
Published in
Frontiers of Mathematics in China

We prove an Artin-Schelter regularity result for the method of twisted tensor products under a certain form. Such twisted tensor products, whose twisting maps are determined by the action on the generators, include Ore extensions and double Ore extensions. It is helpful to construct high-dimensional Artin-Schelter regular algebras.

Pridham, J. P.
Published in
Selecta Mathematica

We prove that every 0-shifted symplectic structure on a derived Artin n-stack admits a curved A∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_{\infty }$$\end{docume...

Tabuada, Gonçalo
Published in
Mathematische Zeitschrift

In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of separably closed fields. As a byproduct, we obtain an extension of Suslin’s rigidity theorem, as well as of Ya...

Craw, Alastair Green, James
Published in
European Journal of Mathematics

We prove that every toric quiver flag variety Y is isomorphic to a fine moduli space of cyclic modules over the algebra End(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docum...

Burban, Igor Drozd, Yuriy Gavran, Volodymyr
Published in
European Journal of Mathematics

We develop the theory of minors of non-commutative schemes. This study is motivated by applications in the theory of non-commutative resolutions of singularities of commutative schemes. In particular, we construct a categorical resolution for non-commutative curves and in the rational case show that it can be realized as the derived category of a q...

Dinh Van, Hoang Liu, Liyu Lowen, Wendy
Published in
Selecta Mathematica

We identify a class of quasi-compact semi-separated (qcss) twisted presheaves of algebras A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document} ...

Rogalski, D. Sierra, S. J. Stafford, J. T.

We develop a ring-theoretic approach for blowing up many noncommutative projective surfaces. Let T be an elliptic algebra (meaning that, for some central element g of degree 1, T/gT is a twisted homogeneous coordinate ring of an elliptic curve E at an infinite order automorphism). Given an effective divisor d on E whose degree is not too big, we co...