TAILIEUCHUNG - Đề tài " Stability conditions on triangulated categories "

This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from . Douglas’s work on Π-stability. From a mathematical point of view, the most interesting feature of the definition is that the set of stability conditions Stab(D) on a fixed category D has a natural topology, thus defining a new invariant of triangulated categories. In a separate article [6] I give a detailed description of this space of stability conditions in the case that D is the bounded derived category of coherent. | Annals of Mathematics Stability conditions on triangulated categories By Tom Bridgeland Annals of Mathematics 166 2007 317 345 Stability conditions on triangulated categories By Tom Bridgeland 1. Introduction This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory and especially from . Douglas s work on n-stability. From a mathematical point of view the most interesting feature of the definition is that the set of stability conditions Stab D on a fixed category D has a natural topology thus defining a new invariant of triangulated categories. In a separate article 6 I give a detailed description of this space of stability conditions in the case that D is the bounded derived category of coherent sheaves on a K3 surface. The present paper though is almost pure homological algebra. After setting up the necessary definitions I prove a deformation result which shows that the space Stab D with its natural topology is a manifold possibly infinite-dimensional. . Before going any further let me describe a simple example of a stability condition on a triangulated category. Let X be a nonsingular projective curve and let D X denote its bounded derived category of coherent sheaves. Recall 11 that any nonzero coherent sheaf E on X has a unique Harder-Narasimhan filtration 0 E0 c E1 c c En-1 c En E whose factors Ej Ej-1 are semistable sheaves with descending slope 1 deg rank. Torsion sheaves should be thought of as having slope rc and come first in the filtration. On the other hand given an object E E D X the truncations ơ j E associated to the standard t-structure on D X fit into triangles j1 E ------ V Aj ơ j E --------- V Aj 1 Ơ j 1 E 318 TOM BRIDGELAND which allow one to break up E into its shifted cohomology sheaves Aj Hj E j . Combining these two ideas one can concatenate the Harder-Narasimhan filtrations of the cohomology sheaves Hj E to obtain a kind of filtration

• Thạc sĩ - Tiến sĩ - Cao học
• Stability conditions
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Acoustic waves
• Finite elements
• Finite spheres
• Inf sup conditions
• Meshfree methods
• INF SUP stability conditions
• Lecture Power system stability
• Bài giảng Ổn định hệ thống điện
• Power system stability
• North American East West Interconnection Study
• Heavy load conditions
• Dynamic model setup
• Vietnam Journal of Mechanics
• On the elastoplastic stability problem
• The thin round cylindrical shells
• Complex loading processes
• The various kinematic boundary conditions
• Biplot graphs
• Yield stability measures
• Wheat genotypes evaluated
• GxE interaction analysis
• Restricted irrigated timely sown conditions
• Grain yield
• Tropical maize (Zea mays L )
• Optimal conditions
• Heat stress
• Traits in tropical maize
• Stability for grain yield
• Genotype x environment
• Stability analysis for yield
• Components in pigeonpea
• Rainfed conditions
• Identify stable genotypes of pigeonpea
• Antimicrobial activity
• Lactobacillus acidophilus
• Heat stability
• pH stability
• Storage stability
• Tạp chí khoa học
• Mobile robots
• Electric wheelchairs
• Stability limit of the vehicle
• Modeling vehicle
• Existence of integro differential equations
• Uniqueness of integro differential equations
• Stability solution of volterra friedholm of integro differential equations
• Volterra friedholm of integro differential equations
• Integro differential equations
• Sufficient conditions on compact spaces
• Water stress
• Relative water content
• Leaf water potential
• Epicuticular wax
• Cell membrane stability
• Chlorophyll stability index
• Super absorbent polymer
• Physiological parameters of maize
• Application of super absorbent polymer
• Carbohydrate polymers
• Colloidal stability
• Physiological conditions
• Isotonic ionic
• Amphipathic chitosans
• BMC Pulmonary Medicine
• Cigarette smoking
• Epidemiologic research
• Exhaled nitric oxide
• Offline measurement
• Storage conditions
• Inverse problems
• Carleman inequality
• Stokes equation
• Stability estimate
• Nonhomogeneous boundary conditions
• Báo cáo sinh học hay
• cách trình bày báo cáo
• báo cáo sinh học
• công trình nghiên cứu sinh học
• tài liệu về sinh học
• trình bày báo cáo
• tài liệu báo cáo khoa học
• báo cáo thú y
• bệnh ở động vật
• nghiên cứu bệnh thú ý
• báo cáo khoa học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• Fundamentals of control systems
• Lecture Fundamentals of control systems
• Analysis of discrete control systems
• Stability conditions for discrete systems
• Extension of Routh Hurwitz criteria
• Jury criterion
• Agronomic traits
• Drought stress
• Photosynthetic efficiency
• Stability index
• Winter wheat cultivar
• Methanation of carbon monoxide
• Carbon monoxide over catalysts NiO/TiO2
• High thermal stability
• Studied conditions
• Optimal average size
• BMC Anesthesiology
• Laryngeal mask airway insertion
• Ketamine propofol mixture
• Supraglottic airway device
• Modern general anesthesia
• Protein stabilization
• Sugar glass
• Dynamic vapor sorption
• Differential scanning calorimetry
• BMC Genetics
• Oriental fruit fly
• Male recombination
• Laboratory adaptation
• Filter rearing system
• Routine monitoring
• Social equality
• Social welfare
• Social justice
• Socioeconomic development
• Socio political stability
• Create favorable conditions