The deepest result in the theory of perverse sheaves on algebraic varieties, the. Moduli of predmodules, perverse sheaves and the riemann. Part i is devoted to dmodule theory, placing special emphasis on holonomic modules and constructible sheaves. Key to dmodules, perverse sheaves, and representation theory is the authors. In the first part, we survey results relating singularities in finite and affine schubert varieties and nilpotent cones to modular representations of reductive groups and their weyl groups.
Part ii representation theory 9 algebraic groups and lie algebras 229 9. The second part is a brief introduction to the theory of perverse sheaves with an emphasis on the case of positive. Dmodules, perverse sheaves, and representation theory ryoshi. This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. Perverse sheaves and modular representation theory arxiv. Perverse sheaves and modular representation theory daniel juteau, carl mautner, and geordie williamson abstract. Dmodules, perverse sheaves, and representation theory.
Dmodule theory and its typical applications to representation theory as we believe that this is a nice way to understand the whole subject. Algebraic geometry, representation theory and topology of singular spaces. Daniel juteau lmno, carl mautner, geordie williamson. Key to dmodules, perverse sheaves, and representation theory is the authors essential algebraicanalytic approach to the theory, which. Dmodules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory key to dmodules, perverse sheaves, and representation theory is the authors essential algebraicanalytic approach to the theory, which connects dmodules to representation theory and other areas of mathematics. Dmodules, perverse sheaves, and representation theory is a greatly expanded translation of the japanese edition entitled d kagun to. This paper is an introduction to the use of perverse sheaves with positive characteristic coe. We also construct a moduli scheme for perverse sheaves on the. Representation theory perverse sheaves lies in the solution of the. Pdf perverse sheaves and modular representation theory. Perverse sheaves in representation theory, besse, france, june 2427, 20. D modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory. Key to dmodules, perverse sheaves, and representation theory is the authors essential algebraicanalytic approach to the theory, which connects d modules to representation theory and other areas of mathematics. Finally, if time allows, we will discuss applications of dmodules in representation theory, namely the beilinsonbernstein localization theorem.
493 624 1174 1323 637 478 843 1358 1619 1606 1360 810 286 379 1272 418 1169 144 913 777 1621 1290 1322 411 444 418 984 999 544 181 423 1422 653 1051 1257 391 743 1069 1088 123 27 1113 143 1114 578 376 74