6 edition of **Higher Dimensional Varieties and Rational Points (Bolyai Society Mathematical Studies)** found in the catalog.

- 67 Want to read
- 34 Currently reading

Published
**August 13, 2003**
by Springer
.

Written in English,

- Algebraic geometry,
- Geometry - General,
- Discrete Mathematics,
- Mathematics,
- Science/Mathematics,
- Rational points (Geometry),
- General,
- Geometry - Algebraic,
- Mathematics / Combinatorics,
- Mathematics / Geometry / Algebraic,
- Mathematics : Discrete Mathematics,
- Medical : General,
- Algebraic varieties,
- Number Theory

**Edition Notes**

Contributions | Károly Jr. Böröczky (Editor), János Kollár (Editor), Tamás Szamuely (Editor) |

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 300 |

ID Numbers | |

Open Library | OL9536639M |

ISBN 10 | 3540008209 |

ISBN 10 | 9783540008200 |

I discuss some arithmetic aspects of higher-dimensional algebraic geometry. I focus on varieties with many rational points and on connections with classification theory and the minimal model by: 5. Publications Books edited [1] Rational points on algebraic varieties, (with E. Peyre), Progress in Mathematics , Birkhäuser, () [2] Arithmetic of higher-dimensional algebraic varieties, (with B. Poonen), Progress in Mathematics , Birkhäuser, () [3] Mathematisches Institut, Seminars /04, Universitätsverlag Göttingen, ().

Free 2-day shipping. Buy Progress in Mathematics: Rational Points on Algebraic Varieties: Zweite, Aktualisierte Und Erweiterte Auflage (Hardcover) at nd: Emmanuel Peyre; Yuri Tschinkel. Key techniques are drawn from the theory of elliptic curves, including modular curves and parametrizations, Heegner points, and heights. The arithmetic of higher-dimensional varieties is equally rich, offering a complex interplay of techniques including Shimura varieties, the minimal model program, moduli spaces of curves and maps, deformation.

Email your librarian or administrator to recommend adding this book to your organisation's collection. Araujo, C. and Kollár, J. Rational curves on varieties. Higher Dimensional Varieties and Rational Points (Budapest, J., Smith, K. E., and Corti, A. Rational and Nearly Rational Varieties. Cambridge Studies in Advanced Mathematics. [Kovacs03c] S. J. Kovács, "Families of varieties of general type: the Shafarevich conjecture and related problems," in Higher Dimensional Varieties and Rational Points, New York: Springer-Verlag, , vol. .

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The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in.

ISBN: OCLC Number: Description: pages ; äc 25 cm. Contents: Rational curves on varieties / Carolina Araujo and Janos Higher Dimensional Varieties and Rational Points book --Rationally connected varieties and fundamental groups / Janos Kollar --Families of varieties of general type / Sandor J.

Kovacs --Points rationnels sur les fibrations / Jean-Louis Colliot-Thelene. Arithmetic of Higher-Dimensional Algebraic Varieties (Progress in Mathematics Book ) - Kindle edition by Poonen, Bjorn, Tschinkel, Yuri.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Arithmetic of Higher-Dimensional Algebraic Varieties (Progress in Mathematics Book ).Manufacturer: Springer.

This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral : Hardcover.

This text, which focuses on higher-dimensional varieties, provides precisely such an interdisciplinary view of the subject. It is a digest of research and survey papers by leading specialists; the book documents current knowledge in higher-dimensional arithmetic and gives indications for future research.

Introductory Workshop in Rational and Integral Points on Higher-Dimensional Varieties: Ma - Ma Cohomological Approaches to Rational Points: - Analytic Methods for Diophantine Equations. Those who downloaded this book also downloaded the following books.

"This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic by: Introductory Workshop in Rational and Integral Points on Higher-Dimensional Varieties Janu - Janu Registration Deadline: Decem over 14 years ago.

Theorem Assume Theorem in dimension ≤ n - 1. Let π: X → Z be a projective morphism from a smooth quasi-projective variety of dimension n to a normal affine variety. Understanding rational points on arbitrary algebraic varieties is the ultimate challenge. We have conjectures but few results.

Poonen's book, with its mixture of basic constructions and openings into current research, will attract new generations to the Queen of Mathematics Jean-Louis Colliot-Thélène, Université Paris-Sud.

3 Rational curves on varieties 33 contents of the book [H]), we present in these notes the necessary material (and a bit more) to understand Mori’s cone theorem. nitely many points, these intersection points with multiplicities. When Dis nef, this is also.

Introduction to rational points Bjorn Poonen University of California at Berkeley MSRI Introductory Workshop on Rational and Integral Points on Higher-dimensional Varieties (organized by Jean-Louis Colliot-Th´el`ene, Roger Heath-Brown, J´anos Koll´ar, Bjorn Poonen, Alice Silverberg, Yuri Tschinkel) Janu File Size: KB.

The subject of this book is the classification theory and geometry of higher dimensional varieties: existence and geometry of rational curves via characteristic p-methods, manifolds with negative Kodaira dimension, vanishing theorems, theory of extremal rays (Mori theory), and minimal models.

Hassett B. () Potential Density of Rational Points on Algebraic Varieties. In: Böröczky K., Kollár J., Szamuely T. (eds) Higher Dimensional Varieties and Rational Cited by: The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points.

This is the natural set-up of the Hasse principle and various approximation properties of Cited by: What kind of book this is The literature on rational points is vast.

To write a book on the subject, an author must 1. write thousands of pages to cover all the topics comprehensively, or 2. focus on one aspect of the subject, or 3. write an extended survey serving as an introduction to many topics,File Size: 1MB. Arithmetic of higher-dimensional algebraic varieties Bjorn Poonen, Yuri Tschinkel One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through.

The book presents the state of the art in computational arithmetic geometry for higher-dimensional algebraic varieties and will be a valuable reference for researchers and graduate students interested in that area. The central theme of this book is the study of rational points on algebraic varieties of Fano and intermediate type—both in.

Next, for the cohomological methods to detect rational points, chapters four to eight give the modern interpretations of Galois descent and the local-to-global principle. For chapter four, on descent theory, the reader is advised to keep chapter six of Bosch, Lütkenbohmert and Raynaud's Néron Models (Springer, ) at hand.

The aim of the Summer School and Conference on Higher Dimensional Varieties and Rational Points held in Budapest, Hungary during September was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in.Education and career.

Yuri Tschinkel attended fromthe Erweiterte Oberschule Heinrich-Hertz-Gymnasium in East Berlin and passed there in the graduated with honors from the Lomonosov Moscow State University in and received his doctorate in from MIT with thesis Rational points on algebraic surfaces under the supervision of Yuri Manin and Michael Artin.Varieties with few rational points.

In higher dimensions, one unifying goal is the Bombieri–Lang conjecture that, for any variety X of general type over a number field k, the set of k-rational points of X is not Zariski dense in X.

(That is, the k-rational points are contained in .