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Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel-Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.

Geometry, Algebraic. --- Géométrie algébrique. --- Algebraic geometry. --- Mathematics --- Geometry --- Algebraic. --- Algebraic geometry

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Homotopy theory. --- Geometry, Algebraic. --- Associative rings. --- Rings (Algebra) --- Homotopie --- Géométrie algébrique --- Anneaux associatifs --- Anneaux (Algèbre) --- Homotopy theory --- Geometry, Algebraic --- Associative rings --- Géométrie algébrique --- Anneaux (Algèbre)

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"D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann-Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Études Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense." [Publisher]

D-modules. --- Modules (Algebra) --- Sheaf theory. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Cohomology, Sheaf --- Sheaf cohomology --- Sheaves, Theory of --- Sheaves (Algebraic topology) --- Algebraic topology --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- D-modules, Théorie des. --- Modules (algèbre) --- Faisceaux, Théorie des. --- Géométrie algébrique.