MARC details
| 000 -LEADER |
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| fixed length control field |
02350 a2200241 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
201030b ||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780691193779 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.35 |
| Item number |
WUS |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Wüstholz, Gisbert (Ed.) |
| 245 ## - TITLE STATEMENT |
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| Title |
Arithmetic and geometry: ten years in Alpbach |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Princeton University Press, |
| Date of publication, distribution, etc |
2019. |
| Place of publication, distribution, etc |
New Jersey: |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
viii, 174 p. ; |
| Other physical details |
pb; |
| Dimensions |
24 cm. |
| 365 ## - TRADE PRICE |
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| Price type code |
USD |
| Price amount |
75.00 |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE |
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| Title |
Annals of mathematics studies; no. 202. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures--which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria--provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces. The second course, taught by Umberto Zannier, addresses the famous Pell equation--not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course, taught by Shou-Wu Zhang, originates in the Chowla-Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross-Zagier formula on Shimura curves and verify the Colmez conjecture on average. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Arithmetical Algebraic Geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Pellian Polynomials |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
p-Adic Geometry |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Fuchs, Clemens(ED.) |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Item type |
Books |
