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by Robert S. Rumely

Download Capacity Theory on Algebraic Curves (Lecture Notes in Mathematics) fb2, epub

ISBN: 3540514104
Author: Robert S. Rumely
Language: English
Publisher: Springer; 1989 edition (August 9, 1989)
Pages: 438
Category: Mathematics
Subcategory: Science
Rating: 4.5
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Size Fb2: 1296 kb
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This book lays foundations for a theory of capacity for adelic sets on algebraic curves.

This book lays foundations for a theory of capacity for adelic sets on algebraic curves. Its main result is an arithmetic one, a generalization of a theorem of Fekete and Szeg? which gives a sharp criterion for algebraic points whose conjugates lie near a specified set on a curve.

Robert Scott Rumely (born 1952) is a professor of mathematics at the University of Georgia who specializes in number theory .

Robert Scott Rumely (born 1952) is a professor of mathematics at the University of Georgia who specializes in number theory and arithmetic geometry  . Capacity Theory on Algebraic Curves (Lecture Notes in Mathematics 1378, 1989).

An ex-library copy bound in brown cloth with paper on-lays to the front and rear covers. Series: Lecture Notes in Mathematics (Book 423). The usual ex-libris markings. The binding is sound and the text is clean. Sold by rowbyrowbookshop. Condition: Used: Good. An ex-library copy bound in brown cloth with paper on-lays to the front and rear covers.

Algebraic Geometry Books. Lecture Notes in Mathematics. This button opens a dialog that displays additional images for this product with the option to zoom in or out. Report incorrect product info or prohibited items. Capacity Theory on Algebraic Curves. Capacity Theory on Algebraic Curves (Lecture Notes in Mathematics).

Capacity theory on algebraic curves, Lecture Notes in Mathematics 1378, Springer-Verlag, New York (1989), 437 p.

Capacity theory on algebraic curves, Lecture Notes in Mathematics 1378, Springer-Verlag, New York (1989), 437 pp. · Existence of the sectional capacity (with C. F. Lau and R. Varley), Memoires of the American Mathematical Society, vol 145, no. 690 (2000), 130 pp. · Potential Theory and Dynamics on the Berkovich Projective Line (with M. Baker), volume 159 in the AMS Surveys and Monographs Series (2010), 428 p.

Definitions of concepts named for Robert Scott Rumely can be found here. 1989: Capacity Theory on Algebraic Curves. 2000: Existence of the Sectional Capacity.

American professor of mathematics specializing in number theory and arithmetic geometry. Definitions of concepts named for Robert Scott Rumely can be found here. 2010: Potential Theory and Dynamics on the Berkovich Projective Line. 2013: Capacity Theory with Local Rationality: The Strong Fekete-Szegö Theorem on Curves.

This is a set of expanded lecture notes from the Berkovich Space seminar held at the University of Georgia during Spring, 2004. Capacity theory on algebraic curves, Robert S. Rumely. The purpose of the notes is to provide a non-technical introduction to Berkovich spaces, and to develop the foundations for analysis on the Berkovich projective line, with a view toward applications in dynamics. Capacity theory and arithmetic intersection theory. Capacity Theory on Algebraic Curves (Lecture Notes in Mathematics 1378, 1989)

Robert Scott Rumely (born 1952) is a professor of mathematics at the University of Georgia who specializes in number theory and arithmetic geometry Contents. Existence of the Sectional Capacity (Memoirs of the American Mathematical Society 145, 2000). Potential Theory and Dynamics on the Berkovich Projective Line (Mathematical Surveys and Monographs 159, 2010).

Algebraic Curves and Projective Geometry - Edoardo Ballico, Ciro Ciliberto . Capacity Theory on Algebraic Curves - Robert S. Rumely (1989) (,,,,,,, . .

Capacity Theory on Algebraic Curves - Robert S. Rumely (1989) (,,,,,,,, ).

Capacity is a measure of size for sets, with diverse applications in potential theory, probability and number theory. This book lays foundations for a theory of capacity for adelic sets on algebraic curves. Its main result is an arithmetic one, a generalization of a theorem of Fekete and Szegö which gives a sharp existence/finiteness criterion for algebraic points whose conjugates lie near a specified set on a curve. The book brings out a deep connection between the classical Green's functions of analysis and Néron's local height pairings; it also points to an interpretation of capacity as a kind of intersection index in the framework of Arakelov Theory. It is a research monograph and will primarily be of interest to number theorists and algebraic geometers; because of applications of the theory, it may also be of interest to logicians. The theory presented generalizes one due to David Cantor for the projective line. As with most adelic theories, it has a local and a global part. Let /K be a smooth, complete curve over a global field; let Kv denote the algebraic closure of any completion of K. The book first develops capacity theory over local fields, defining analogues of the classical logarithmic capacity and Green's functions for sets in (Kv). It then develops a global theory, defining the capacity of a galois-stable set in (Kv) relative to an effictive global algebraic divisor. The main technical result is the construction of global algebraic functions whose logarithms closely approximate Green's functions at all places of K. These functions are used in proving the generalized Fekete-Szegö theorem; because of their mapping properties, they may be expected to have other applications as well.

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