Ebook: Arithmetic and Geometry Around Galois Theory

This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.​

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This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on ?tale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.

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This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on ?tale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.
Content:
Front Matter....Pages i-xi
Algebraic Stacks with a View Toward Moduli Stacks of Covers....Pages 1-148
Models of Curves....Pages 149-170
Galois Categories....Pages 171-246
Fundamental Groupoid Scheme....Pages 247-286
Extension of Galois Groups by Solvable Groups, and Application to Fundamental Groups of Curves....Pages 287-304
On the “Galois Closure” for Finite Morphisms....Pages 305-325
Hasse Principle and Cohomology of Groups....Pages 327-335
Periods of Mixed Tate Motives, Examples, l-adic Side....Pages 337-369
On Totally Ramified Extensions of Discrete Valued Fields....Pages 371-376
An Octahedral Galois-Reflection Tower of Picard Modular Congruence Subgroups....Pages 377-401

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This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on ?tale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.
Content:
Front Matter....Pages i-xi
Algebraic Stacks with a View Toward Moduli Stacks of Covers....Pages 1-148
Models of Curves....Pages 149-170
Galois Categories....Pages 171-246
Fundamental Groupoid Scheme....Pages 247-286
Extension of Galois Groups by Solvable Groups, and Application to Fundamental Groups of Curves....Pages 287-304
On the “Galois Closure” for Finite Morphisms....Pages 305-325
Hasse Principle and Cohomology of Groups....Pages 327-335
Periods of Mixed Tate Motives, Examples, l-adic Side....Pages 337-369
On Totally Ramified Extensions of Discrete Valued Fields....Pages 371-376
An Octahedral Galois-Reflection Tower of Picard Modular Congruence Subgroups....Pages 377-401
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