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Super QVNTS: Kummer Classes and Anabelian Geometry September 10-11, 2016
URLﾘﾝｸ(www.uvm.edu)
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KUMMER CLASSES AND ANABELIAN GEOMETRY JACKSON S. MORROW Date: April 29, 2017.
ABSTRACT. These notes comes from the Super QVNTS: Kummer Classes and Anabelian
geometry. Any virtues in the notes are to be credited to the lecturers and not the scribe;
however, all errors and inaccuracies should be attributed to the scribe. That being said,
I apologize in advance for any errors (typo-graphical or mathematical) that I have introduced.
CONTENTS
1. On Mochizuki’s approach to Diophantine inequalities
Lecturer: Kiran Kedlaya . . . . . . 2
2. Why the ABC Conjecture?
Lecturer: Carl Pomerance . . . . . 3
3. Kummer classes, cyclotomes, and reconstructions (I/II)
Lecturer: Kirsten Wickelgren . . . . . 3
4. Kummer classes, cyclotomes, and reconstructions (II/II)
Lecturer: David Zureick-Brown . . . . . 6
5. Overflow session: Kummer classes
Lecturer: Taylor Dupuy . . . . . 8
6. Introduction to model Frobenioids
Lecturer: Andrew Obus . . . . . 11
7. Theta functions and evaluations
Lecturer: Emmanuel Lepage . . . . . . 13
8. Roadmap of proof
Notes from an email from Taylor Dupuy . . . . 17
References . . . . . . 19
6. INTRODUCTION TO MODEL FROBENIOIDS
LECTURER: ANDREW OBUS
By way of introduction, Mochizuki loosely defines a Frobenioid as a category theoretic abstraction of divisors or line bundles on a geometry object.
Our main example will be an abstract category which encodes etale coverings and information concerning divisors.