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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**Book Description **American Mathematical Society, United States, 2002. Hardback. Book Condition: New. Language: English . Brand New Book. 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. Bookseller Inventory # AAN9780821820360

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Published by
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ISBN 10: 0821820362
ISBN 13: 9780821820360

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**Book Description **American Mathematical Society, United States, 2002. Hardback. Book Condition: New. Language: English . Brand New Book. 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. Bookseller Inventory # AAN9780821820360

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