Analytic D-Modules and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytic D-Modules and Applications write by Jan-Erik Björk. This book was released on 2013-06-29. Analytic D-Modules and Applications available in PDF, EPUB and Kindle. This is the first monograph to be published on analytic D-modules and it offers a complete and systematic treatment of the foundations together with a thorough discussion of such modern topics as the Riemann--Hilbert correspondence, Bernstein--Sata polynomials and a large variety of results concerning microdifferential analysis. Analytic D-module theory studies holomorphic differential systems on complex manifolds. It brings new insight and methods into many areas, such as infinite dimensional representations of Lie groups, asymptotic expansions of hypergeometric functions, intersection cohomology on Kahler manifolds and the calculus of residues in several complex variables. The book contains seven chapters and has an extensive appendix which is devoted to the most important tools which are used in D-module theory. This includes an account of sheaf theory in the context of derived categories, a detailed study of filtered non-commutative rings and homological algebra, and the basic material in symplectic geometry and stratifications on complex analytic sets. For graduate students and researchers.
The Heart of Cohomology
The Heart of Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Heart of Cohomology write by Goro Kato. This book was released on 2006-11-08. The Heart of Cohomology available in PDF, EPUB and Kindle. If you have not heard about cohomology, The Heart of Cohomology may be suited for you. The book gives Fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived categories are explained in elementary fashion. Applications to sheaf cohomology. In addition, the book examines cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family.
Mixed Twistor D-modules
Mixed Twistor D-modules - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mixed Twistor D-modules write by Takuro Mochizuki. This book was released on 2015-08-19. Mixed Twistor D-modules available in PDF, EPUB and Kindle. We introduce mixed twistor D-modules and establish their fundamental functorial properties. We also prove that they can be described as the gluing of admissible variations of mixed twistor structures. In a sense, mixed twistor D-modules can be regarded as a twistor version of M. Saito's mixed Hodge modules. Alternatively, they can be viewed as a mixed version of the pure twistor D-modules studied by C. Sabbah and the author. The theory of mixed twistor D-modules is one of the ultimate goals in the study suggested by Simpson's Meta Theorem and it would form a foundation for the Hodge theory of holonomic D-modules which are not necessarily regular singular.
D-Modules, Perverse Sheaves, and Representation Theory
D-Modules, Perverse Sheaves, and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook D-Modules, Perverse Sheaves, and Representation Theory write by Kiyoshi Takeuchi. This book was released on 2007-10-12. D-Modules, Perverse Sheaves, and Representation Theory available in PDF, EPUB and Kindle. D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
D-modules and Microlocal Calculus
D-modules and Microlocal Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook D-modules and Microlocal Calculus write by Masaki Kashiwara. This book was released on 2003. D-modules and Microlocal Calculus available in PDF, EPUB and Kindle. Masaki Kashiwara is undoubtedly one of the masters of the theory of $D$-modules, and he has created a good, accessible entry point to the subject. The theory of $D$-modules is a very powerful point of view, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. It is often used in conjunction with microlocal analysis, as some of the important theorems are best stated or proved using these techniques. The theory has been used very successfully in applications to representation theory. Here, there is an emphasis on $b$-functions. These show up in various contexts: number theory, analysis, representation theory, and the geometry and invariants of prehomogeneous vector spaces. Some of the most important results on $b$-functions were obtained by Kashiwara. A hot topic from the mid '70s to mid '80s, it has now moved a bit more into the mainstream. Graduate students and research mathematicians will find that working on the subject in the two-decade interval has given Kashiwara a very good perspective for presenting the topic to the general mathematical public.
