Arithmetic and Geometry (Paperback)

Idioma: inglés

Editorial: Princeton University Press, New Jersey, 2019

0691193770 / 9780691193779

Serie: Libro 193 de 202 - Annals of Mathematics Studies

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Paperback. 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. 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: Shimu This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.…

N° de ref. del artículo 9780691193779

Título
Arithmetic and Geometry (Paperback)
Autor
Gisbert Wuestholz
Editorial
Princeton University Press, New Jersey
Año de publicación
2019
Estado
new
Encuadernación
Paperback
Idioma
inglés
ISBN 10
0691193770
ISBN 13
9780691193779
Serie
Libro 193 de 202: Annals of Mathematics Studies

CitiRetail

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Vendedor de IberLibro desde 29 de junio de 2022

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Primer artículoEUR 44,33EUR 44,33
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