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 book mentioned by Felipe is available here: Grothendieck also conjectured the existence of higher-dimensional anabelian varieties, but these are still very mysterious. By using this site, you agree to the Terms of Use feometry Privacy Policy. No it is a collection of conference talksbut this is also a good source. Caen, Caen,pp.

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.

I want to study anabelian geometry, but unfortunately I’m having difficulties in finding some materials about it. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand anableian Terms of Service. There is this very beautiful survey Nakamura, Hiroaki; Tamagawa, Akio; Mochizuki, Shinichi The Grothendieck conjecture on the fundamental groups of algebraic curves http: The classification of anabelian varieties for number fields was shown in.

A concrete example is the case of curves, which may be affine as well as projective. MathOverflow works best with JavaScript enabled. Anabelian geometry study materials?

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.

More recently, Mochizuki introduced and developed a so called mono-anabelian geometry which restores, for a certain class of hyperbolic curves over number fields, the anabelizn from its algebraic fundamental group. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

This page was last edited on 25 Decemberat Isomorphisms of Galois groupsJ.

### Anabelian geometry – Wikipedia

If you’d like videos, here is a series of lectures on related topics, including a long series by Pop on anabelian geometry. Frans Oort, Lecture notes. Grothendieck conjectured that the algebraic fundamental group G of Ca profinite groupgeometey C itself i. By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

Key results of mono-anabelian geometry were published in Mochizuki’s “Topics in Absolute Anabelian Geometry.

## 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.