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190
DIMENSIONS OF TRIANGULATED CATEGORIES VIA KOSZUL OBJECTS
"... Abstract. Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin alge ..."
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Abstract. Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin algebras. 1.
Motivic structures in noncommutative geometry. Available at arXiv:1003.3210
 the Proceedings of the ICM
, 2010
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THE HALL ALGEBRA OF A SPHERICAL OBJECT
"... Abstract. We determine the Hall algebra, in the sense of Toën, of the algebraic triangulated category generated by a spherical object. 1. ..."
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Abstract. We determine the Hall algebra, in the sense of Toën, of the algebraic triangulated category generated by a spherical object. 1.
Algebraic versus topological triangulated categories
 THE WORKSHOP ON TRIANGULATED CATEGORIES AT THE UNIVERSITY OF LEEDS, AUGUST 13–19
, 2006
"... These are extended and updated notes of a talk, the first version of which I gave at ..."
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Cited by 17 (5 self)
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These are extended and updated notes of a talk, the first version of which I gave at
HOMOLOGICAL MIRROR SYMMETRY FOR PUNCTURED SPHERES
"... Abstract. We prove that the wrapped Fukaya category of a punctured sphere (S2 with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror LandauGinzburg model, proving one side of the homological mirror symmetry conjecture in this case. By in ..."
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Abstract. We prove that the wrapped Fukaya category of a punctured sphere (S2 with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror LandauGinzburg model, proving one side of the homological mirror symmetry conjecture in this case. By investigating fractional gradings on these categories, we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the LandauGinzburg model. 1.
Triangulated categories without models
, 2007
"... We exhibit examples of triangulated categories which are neither ..."
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Cited by 16 (6 self)
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We exhibit examples of triangulated categories which are neither
Homotopy theory of spectral categories
, 2009
"... We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue ..."
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Cited by 16 (6 self)
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We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue
A guided tour through the garden of noncommutative motives
, 2011
"... These are the extended notes of a survey talk on noncommutative motives given at the 3 era Escuela de Inverno Luis SantalóCIMPA Research ..."
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Cited by 15 (6 self)
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These are the extended notes of a survey talk on noncommutative motives given at the 3 era Escuela de Inverno Luis SantalóCIMPA Research
THE BAR DERIVED CATEGORY OF A CURVED DG ALGEBRA
, 2008
"... Curved A∞algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A∞algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras via the bar construction and produce Quillen model structures on their module ..."
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Cited by 15 (2 self)
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Curved A∞algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A∞algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras via the bar construction and produce Quillen model structures on their module categories. We define the analogue of the relative derived category for a curved dg algebra.