New PDF release: D-Modules, Perverse Sheaves, and Representation Theory

By Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki

ISBN-10: 081764363X

ISBN-13: 9780817643638

ISBN-10: 0817645233

ISBN-13: 9780817645236

D-modules is still an lively sector of stimulating learn in such mathematical parts as algebra, research, differential equations, and illustration thought.

Key to D-modules, Perverse Sheaves, and illustration Theory is the authors' crucial algebraic-analytic method of the idea, which connects D-modules to illustration idea and different parts of arithmetic. major strategies and subject matters that experience emerged during the last few a long time are awarded, together with a therapy of the speculation of holonomic D-modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the answer to the Kazhdan-Lusztig conjecture utilizing D-module theory.

To additional relief the reader, and to make the paintings as self-contained as attainable, appendices are supplied as history for the speculation of derived different types and algebraic forms. The booklet is meant to serve graduate scholars in a lecture room environment and as self-study for researchers in algebraic geometry, and illustration theory.

Show description

Read or Download D-Modules, Perverse Sheaves, and Representation Theory PDF

Similar abstract books

Applied Algebraic Dynamics (De Gruyter Expositions in - download pdf or read online

This monograph provides fresh advancements of the idea of algebraic dynamical structures and their functions to desktop sciences, cryptography, cognitive sciences, psychology, picture research, and numerical simulations. an important mathematical effects offered during this e-book are within the fields of ergodicity, p-adic numbers, and noncommutative teams.

Get Exercises for Fourier Analysis PDF

Fourier research is an crucial software for physicists, engineers and mathematicians. a large choice of the recommendations and purposes of fourier research are mentioned in Dr. Körner's hugely well known booklet, An advent to Fourier research (1988). during this ebook, Dr. Körner has compiled a set of workouts on Fourier research that might completely try out the reader's knowing of the topic.

Additional info for D-Modules, Perverse Sheaves, and Representation Theory

Sample text

Since our sheaf DX is locally free over OX , it is quasicoherent over OX . We mainly deal with DX -modules which are quasi-coherent over OX . 1. For an algebraic variety X we denote the category of quasi-coherent OX -modules by Mod qc (OX ). For a smooth algebraic variety X we denote by Mod qc (DX ) the category of OX -quasi-coherent DX -modules. The category Mod qc (DX ) is an abelian category. It is well known that for affine algebraic varieties X, (a) the global section functor (X, •) : Mod qc (OX ) → Mod( (X, OX )) is exact, (b) if (X, M) = 0 for M ∈ Mod qc (OX ), then M = 0.

15. Assume that X is D-affine. Then for any M ∈ Mod qc (DX ) and i > 0 we have H i (X, M) = 0. Proof. 14 we can take a resolution 0 → M → I0 → I1 → · · · , where Ij are injective objects of Mod qc (DX ) which are flabby. Since Ij are flabby, H i (X, M) is the ith cohomology group of the complex (X, I · ). On the other hand since X is D-affine, the functor (X, •) is exact on Mod qc (DX ), and hence H i (X, M) = 0 for i > 0. , [Ha2, p. 126]). 16. (i) Let F be a quasi-coherent OX -module. For an open subset U ⊂ X consider a coherent OU -submodule G ⊂ F |U of the restriction F |U of F to U .

Namely, a candidate for the direct image Mod(DX ) → Mod(DY ) is obtained by the commutativity of Mod(DX ) −−−−→ Mod(DY ) ⏐ ⏐ ⏐ ⏐ ⊗ (•) X ⊗OX Y op OY (•) op Mod(DX ) −−−−→ Mod(DY ) where the lower horizontal arrow is given by f∗ ((•) ⊗DX DX→Y ). Thus, to a a left DX -module M we can associate a left DY -module ⊗−1 Y ⊗OY f∗ (( ⊗OX M) ⊗DX DX→Y ). 11 we have an isomorphism ( of right f −1 D X ⊗OX M) ⊗DX DX→Y Y -modules, where f −1 D ( Y ((ω ⊗ R) ⊗ s)P = (ω ⊗ RP ) ⊗ s X ⊗OX DX→Y ) ⊗DX M acts on ( (ω ∈ X X, R ⊗OX DX→Y ) ⊗DX M by ∈ DX→Y , s ∈ M, P ∈ DY ).

Download PDF sample

D-Modules, Perverse Sheaves, and Representation Theory by Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki


by Ronald
4.5

Rated 4.26 of 5 – based on 31 votes