Arithmetic Fundamental Groups and Noncommutative Algebra is popular PDF and ePub book, written by Michael D. Fried in 2002, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Arithmetic Fundamental Groups and Noncommutative Algebra can be Read Online from any device for your convenience.
Arithmetic Fundamental Groups and Noncommutative Algebra Book PDF 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.
Detail Book of Arithmetic Fundamental Groups and Noncommutative Algebra PDF
- Author : Michael D. Fried
- Release : 30 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821820360
- Genre : Mathematics
- Total Page : 602 pages
- Language : English
- PDF File Size : 8,6 Mb
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