Plan. Fields and projective geometry. Milnor K-theory and Galois cohomology. Almost Abelian Anabelian geometry – Bogomolov’s program. Introduction. view of the goal of understanding to what extent the anabelian geometry of hyperbolic curves over p-adic local fields can be made “absolute”. Our main result . Abstract. This paper forms the first part of a three-part series in which we treat various topics in absolute anabelian geometry from the point of view of develop-.
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The first traditional conjectures, originating from Alexander Grothendieck and introduced in Esquisse d’un Programme were about how topological homomorphisms between two groups of two hyperbolic curves over number fields correspond to maps between the curves.
Views Read Edit View history. The article Matsumoto, Makoto, Arithmetic fundamental groups and moduli of curves. Suppose given a hyperbolic curve Ci. Sign up using Facebook. Sign up or log in Sign up using Google. Florian Pop, Lectures on Anabelian phenomena in geometry and arithmetic pdf Yuri Tschinkel, Introduction to anabelian geometrytalk at Symmetries and correspondences in number theory, geometry, algebra, physics: These Grothendieck conjectures were partially solved by Hiroaki Nakamura and Akio Tamagawa, while complete proofs were given by Shinichi Mochizuki.
For algebraic curves over finite fieldsover number anabeliaan and over p-adic field the statement was eventually completed by Mochizuki This volumeGalois Groups and Fundamental Groupsedited by Leila Schneps has a great collection of geometgy, as does this volumeGeometric Galois Actionsincluding a nice article by Florian Pop on “Glimpses of Grothendieck’s anabelian geometry. Yuri Tschinkel, Introduction to anabelian geometrytalk at Symmetries and correspondences in number theory, geometry, algebra, physics: At MSRI, you can find some lectures from Fallincluding one specifically about anabelian geometry.
This page was last edited on 25 Decemberat Isomorphisms of Galois groupsJ.
Anabelian geometry – Wikipedia
Key results of mono-anabelian geometry were published in Mochizuki’s “Topics in Absolute Anabelian Geometry.
Anabelian geometry is a theory in number theorywhich describes the way to which algebraic fundamental gwometry G of a certain arithmetic variety Vor some related geometric object, can help to restore V. In anabelian geometry one studies how much information about a space X X specifically: Uchida, Isomorphisms of Galois groups of algebraic function fieldsAnn. If you start with Szamuely as an introduction, you could then move on to this afterwards.
Kummer Classes and Anabelian Geometry aanbelian.
I don’t recommend that book. Home Questions Tags Users Unanswered. Taylor DuypuyAnabelian geometry.
That is quite a list of authors. This was eventually proven by various authors in various cases. There are lots of errors even concerning basic definitions and inconsistencies. An early conjecture motivating the theory in Grothendieck 84 was that all hyperbolic curves over number fields are anabelian varieties.
Florian Pop, Lectures on Anabelian phenomena in geometry and arithmetic pdf. Jones’ theoremDeligne-Kontsevich conjecture.
David Corwin 6, 6 66 Matsumoto, Makoto, Arithmetic fundamental groups and moduli of curves.