Proceedings of Symposia in Pure Mathematics Vol. 70. xxx, 569 p. 26 cm. Burgundy cloth. Ex library with labels on spine and covers, ink stamps on top edge and title. Corners bumped, creases in upper spine. 1999 von Neumann Conference on Arithmetic Fundamental Groups and Noncommutative Algebra August 1999, Mathematical Sciences Research Institute, Berkeley.

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Detalles bibliogr�ficos

T�tulo

Arithmetic Fundamental Groups and Noncommutative Algebra

Editor

American Mathematical Society, Providence

Fecha de publicaci�n

1999

ISBN 10

0821820362

ISBN 13

9780821820360

Encuadernaci�n

Hardcover

Estado

ex library-good

Cat�logos de vendedores

Science

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Sinopsis

The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade. The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group $G {\mathbb Q $ of the algebraic numbers and its close relatives. By analyzing how $G {\mathbb Q $ acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s. Papers in Part 2 apply $\theta$-functions and configuration spaces to the study of fundamental groups over positive characteristic fields. In this section, several authors use Grothendieck's famous lifting results to give extensions to wildly ramified covers. Properties of the fundamental groups have brought collaborations between geometers and group theorists. Several Part 3 papers investigate new versions of the genus 0 problem. In particular, this includes results severely limiting possible monodromy groups of sphere covers. Finally, Part 4 papers treat Deligne's theory of Tannakian categories and arithmetic versions of the Kodaira-Spencer map. This volume is geared toward graduate students and research mathematicians interested in arithmetic algebraic geometry.

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