مدول‌های جبری (چشم‌اندازهایی در ریاضیات؛ جلد ۲)

Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry. Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry. Catégories dérivées et foncteurs dérivés / by P.-P. Grival Coherent D-modules / by B. Kaup Local theory of meromorphic connections in dimension one (Fuchs theory) / by A. Haefliger Regular connections after Deligne / by B. Malgrange The Weyl algebra / by F. Ehlers Operations on algebraic D-modules ; Coherent, holonomic, and regular holonomic complexes ; The Riemann-Hilbert correspondence / by A. Borel.