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Arithmetic fundamental groups and noncommutative algebra : 1999 von Neumann Conference on Arithmetic Fundamental Groups and Noncommutative Algebra, August 16-27, 1999, Mathematical Sciences Research Institute, Berkeley, California / Michael D. Fried, Yasutaka Ihara, editors.
- Format:
- Book
- Conference/Event
- Author/Creator:
- Von Neumann Conference on Arithmetic Fundamental Groups and Noncommutative Algebra, Corporate Author.
- Conference Name:
- Von Neumann Conference on Arithmetic Fundamental Groups and Noncommutative Algebra (1999 : Berkeley, Calif.), issuing body.
- Series:
- Proceedings of symposia in pure mathematics ; volume 70.
- Proceedings of symposia in pure mathematics, 0082-0717 ; volume 70
- Language:
- English
- Subjects (All):
- Fundamental groups (Mathematics)--Congresses.
- Fundamental groups (Mathematics).
- Noncommutative algebras--Congresses.
- Noncommutative algebras.
- Physical Description:
- 1 online resource (602 p.)
- Other Title:
- Arithmetic fundamental groups
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2002]
- Language Note:
- English
- Summary:
- 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.
- Contents:
- ""Contents""; ""Prelude: Arithmetic fundamental groups and noncommutative algebra""; ""Part 1. G[sub(Q)] action on moduli spaces of covers""; ""Descent theory for algebraic covers""; ""Galois invariants of dessins d'enfants""; ""Limits of Galois representations in fundamental groups along maximal degeneration of marked curves, II""; ""Hurwitz monodromy, spin separation and higher levels of a modular tower""; ""Field of moduli and field of definition of Galois covers""; ""Relationships between conjectures on the structure of pro-p Galois groups unramified outside p""
- ""Galois realizations of profinite projective linear groups""""Part 4. Fundamental groupoids and Tannakian categories""; ""Semisimple triangular Hopf algebras and Tannakian categories""; ""On a theorem of Deligne on characterization of Tannakian categories""; ""A survey of the Hodge-Arakelov theory of elliptic curves I""
- Notes:
- Description based upon print version of record.
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 0-8218-9375-0
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