Rigid Geometry Of Curves And Their Jacobians PDF Download
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| Author | : Werner Lütkebohmert |
| Publisher | : Springer |
| Total Pages | : 386 |
| Release | : 2016-01-26 |
| Genre | : Mathematics |
| ISBN | : 331927371X |
Download Rigid Geometry of Curves and Their Jacobians Book in PDF, ePub and Kindle
This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
| Author | : David Mumford |
| Publisher | : Ann Arbor : University of Michigan Press, c1975, 1976 printing. |
| Total Pages | : 120 |
| Release | : 1975 |
| Genre | : Mathematics |
| ISBN | : |
Download Curves and Their Jacobians Book in PDF, ePub and Kindle
| Author | : Jean Fresnel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 303 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461200415 |
Download Rigid Analytic Geometry and Its Applications Book in PDF, ePub and Kindle
Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.
| Author | : Bruno Anglès |
| Publisher | : Springer Nature |
| Total Pages | : 337 |
| Release | : 2021-03-03 |
| Genre | : Mathematics |
| ISBN | : 3030662497 |
Download Arithmetic and Geometry over Local Fields Book in PDF, ePub and Kindle
This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.
| Author | : E. Arbarello |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 416 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : |
Download Geometry of Algebraic Curves Book in PDF, ePub and Kindle
This comprehensive and self-contained account of the extrinsic geometry of algebraic curves applies the theory of linear series to a number of classical topics, including the geometry of the Reimann theta divisor, as well as to contemporary research.
| Author | : Günter Harder |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 376 |
| Release | : 2011-04-21 |
| Genre | : Mathematics |
| ISBN | : 3834881597 |
Download Lectures on Algebraic Geometry II Book in PDF, ePub and Kindle
This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.
| Author | : Mark Adler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 487 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 366205650X |
Download Algebraic Integrability, Painlevé Geometry and Lie Algebras Book in PDF, ePub and Kindle
This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.
| Author | : A.N. Parshin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 275 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662036622 |
Download Algebraic Geometry III Book in PDF, ePub and Kindle
This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.
| Author | : Kazuhiro Fujiwara |
| Publisher | : |
| Total Pages | : 863 |
| Release | : 2018 |
| Genre | : MATHEMATICS |
| ISBN | : 9783037196359 |
Download Foundations of Rigid Geometry I Book in PDF, ePub and Kindle
Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate's rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Nowadays, rigid geometry is a discipline in its own right and has acquired vast and rich structures, based on discoveries of its relationship with birational and formal geometries. In this research monograph, foundational aspects of rigid geometry are discussed, putting emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion on the relationship with Tate's original rigid analytic geometry, V.G. Berkovich's analytic geometry and R. Huber's adic spaces. As a model example of applications, a proof of Nagata's compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost self-contained.
| Author | : M. Audin |
| Publisher | : Cambridge University Press |
| Total Pages | : 156 |
| Release | : 1999-11-13 |
| Genre | : Mathematics |
| ISBN | : 9780521779197 |
Download Spinning Tops Book in PDF, ePub and Kindle
Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established iby many mathematicians. This book presents some of these techniques, which fall within the orbit of finite dimensional integrable systems. The main body of the text presents a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics, whilst in appendices the general, abstract theory is described. The methods are given a topological application to the study of Liouville tori and their bifurcations. The book is based on courses for graduate students given by the author at Strasbourg University but the wealth of original ideas will make it also appeal to researchers.
