TAILIEUCHUNG - Đề tài " Localization of modules for a semisimple Lie algebra in prime characteristic "

We show that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized) regular central character are the same as coherent sheaves on the formal neighborhood of the corresponding (generalized) Springer fiber. | Annals of Mathematics Localization of modules for a semisimple Lie algebra in prime characteristic By Roman Bezrukavnikov Ivan Mirkovi c and Dmitriy Rumynin Annals of Mathematics 167 2008 945 991 Localization of modules for a semisimple Lie algebra in prime characteristic By Roman Bezrukavnikov Ivan Mirkovic and DMiTRiy RuMyNiN Abstract We show that on the level of derived categories representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given generalized regular central character are the same as coherent sheaves on the formal neighborhood of the corresponding generalized Springer fiber. The first step is to observe that the derived functor of global sections provides an equivalence between the derived category of P-modules with no divided powers on the flag variety and the appropriate derived category of modules over the corresponding Lie algebra. Thus the derived version of the Beilinson-Bernstein localization theorem holds in sufficiently large positive characteristic. Next one finds that for any smooth variety this algebra of differential operators is an Azumaya algebra on the cotangent bundle. In the case of the flag variety it splits on Springer fibers and this allows us to pass from P-modules to coherent sheaves. The argument also generalizes to twisted P-modules. As an application we prove Lusztig s conjecture on the number of irreducible modules with a fixed central character. We also give a formula for behavior of dimension of a module under translation functors and reprove the Kac-Weisfeiler conjecture. The sequel to this paper BMR2 treats singular infinitesimal characters. To Boris Weisfeiler missing since 1985 Contents Introduction 1. Central reductions of the envelope PX of the tangent sheaf . Frobenius twist . The ring of crystalline differential operators Px . The difference I of pth power maps on vector fields . Central reductions . was partially supported by NSF grant .

• Thạc sĩ - Tiến sĩ - Cao học
• Localization
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• International Journal of Computer Networks and Communications Security
• Combined localization synchronization method for underwater communication
• Combined localization synchronization method
• The proposed method
• Well known method
• Prototype data showed
• Router aided approach
• Hierarchical traffic localization
• Bandwidth limitation
• P2P traffic localization
• P2P system
• Physical network topology
• Nuclear engineering and technology
• Leak detection and 3D source localization method
• 3D source localization method on a plant piping system
• 3D leakage location
• The detected leakage area
• Visual Simultaneous Localization and Mapping
• Indoor 3D topographical
• 3D Topographical and radiological mapping
• Near real time radioactive sources
• Simultaneous Localization and Mapping
• Localization technologies
• Indoor environment
• Localization technologies for indoor environment
• Indoor environments are high accuracy
• Low latency
• Autonomous Map Building
• Navigation
• Mobile Robot Kinematics
• Mobile Robot Localization
• Localization Systems
• Control localization
• Brain source localization using EEG signal analysis
• Signal analysis
• EEG inverse problem
• Bayesian techniques
• Results and comparison
• Future directions for EEG source localization
• BMC Bioinformatics
• Essential proteins
• Protein protein interaction network
• Subcellular localization
• Cellular survival
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• LOCALIZATION STRATEGIES BLEM
• NATURAL LANGUAGE FRONT ENDS
• Lance A
• Remshaw
• scientific reports
• model language
• process natural language
• EEG inverse problem I
• Classical techniques
• Hybrid techniques
• Head modeling approaches
• Localization in clinical neurology
• Clinical neurology
• General principles
• The lumbosacral plexus
• Lumbosacral plexuses
• Spinal cord
• the cerebellum
• Lesions affecting the hypothalamus
• The cerebral hemispheres
• The autonomic nervous system
• In situ localization
• Germin gene
• Auxin induced callus formation
• Digoxigenin labeled germin sense
• Anti sense RNA probes
• Vietnam Journal of Mechanics
• Finite element simulation of strain localization
• Inelastic solids by energy relaxation
• Demonstrated through numerical simulation
• The structure leads
• Journal of Automation and Control Engineering
• EKF based localization
• Mobile robot using pattern matching
• Chirp spread spectrum
• The multi path effect
• The extended Kalman filter
• Cerebral cortex
• Trehalase localization
• The cerebral cortex
• Hippocampus of mouse brains
• Cerebellum of mouse brains
• Leak detection and localization
• Acoustic emission technique
• Method of acoustic emission
• AE characteristic parameters
• Geometrical axis
• Corneal apex
• Computer aided design
• Minimum corneal thickness point
• Spatial localization
• Morphogeometric analysis
• BMC Plant Biology
• Histone deacetylases
• Gene expression
• Abiotic stresses
• Sheep ovary
• Goat ovary
• Follicular development
• Ovaries of sheep and goat
• Immunohistochemical localization
• Proliferating cell nuclear antigen
• BMC Cancer
• Papillary thyroid microcarcinoma
• Immunohistochemical analysis
• Ep ICD subcellular localization index
• Metastatic papillary thyroid microcarcinoma
• Template matching
• Object recognition
• Object localization
• Pattern recognition
• Driver genes
• Random walk
• Variation frequency
• Dysregulated genes
• Genomic expression