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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This page was last edited on 25 Decemberat Isomorphisms of Galois groupsJ. 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. Anabelian geometry is a theory in number theorywhich describes the way to which algebraic fundamental group G of a certain arithmetic variety Vor some related geometric object, can help to restore V.

## Anabelian geometry

If you start with Szamuely as an introduction, you could then move on to this afterwards. MathOverflow works best with JavaScript enabled. By using this site, you agree to the Terms of Use and Privacy Policy. Key results of mono-anabelian geometry were published in Mochizuki’s “Topics in Absolute Anabelian Geometry. There is this very beautiful survey Nakamura, Hiroaki; Tamagawa, Akio; Mochizuki, Shinichi The Grothendieck conjecture on the fundamental groups of algebraic curves http: The article Matsumoto, Makoto, Arithmetic anabeliian groups and moduli of curves.

Suppose given a hyperbolic curve Ci. This was proved by Mochizuki. Views Read Edit View history. The classification of anabelian varieties for anabeliwn fields was shown in. 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. From Wikipedia, gemoetry free encyclopedia.

Notes, 1, Abdus Salam Int. Qnabelian 3, 12 I want to study anabelian geometry, but unfortunately I’m having difficulties in finding some materials about it.

### anabelian geometry in nLab

Florian Pop, Lectures on Anabelian phenomena in geometry and arithmetic pdf. This volumeGalois Groups and Fundamental Groupsedited by Leila Schneps has a great collection of articles, as does this anabrlianGeometric Galois Actionsincluding a nice article by Florian Pop on “Glimpses of Grothendieck’s anabelian geometry.

By using our site, you acknowledge that you have anabelixn and understand our Cookie PolicyPrivacy Policyand our Terms of Service. That is quite a list of authors. Retrieved from ” https: Email Required, but never shown.

Sign up or log in Sign up using Google. These Grothendieck conjectures were partially solved by Hiroaki Nakamura and Akio Tamagawa, while complete proofs were given by Shinichi Mochizuki. Grothendieck conjectured that the algebraic fundamental group G of Ca profinite groupdetermines C itself i.

There are lots of errors even concerning basic definitions and inconsistencies. In anabelian geometry one studies how much information about a space X X specifically: I’m sure this book will be the one to get, once it comes out. Caen, Caen,pp. Autumn Kent 9, 3 45 For algebraic curves over finite fieldsover number fields anabeelian over p-adic field the statement was eventually completed by Mochizuki 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 geommetry to these policies.

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Kummer Classes and Anabelian Geometry pdf. A relation with the theory of motive s is in.

### Anabelian geometry – Wikipedia

I don’t recommend that book. Post as a guest Name. No geomrtry is a collection of conference talksbut this is also a good source. Uchida, Isomorphisms of Galois groups of algebraic function fieldsAnn.

The book mentioned by Felipe is available here: Frans Oort, Lecture notes. In Uchida and Neukirch it was shown that an isomorphism between Galois groups of number fields implies the existence of an isomorphism between those number fields. This was eventually proven by various authors in various gelmetry.

If you’d like videos, here is a series of lectures on related topics, including a long series by Pop on anabelian geometry.

A concrete example is the case of curves, which may be affine as well as projective. Matsumoto, Makoto, Arithmetic fundamental groups and moduli of curves.

Anabelian geometry study materials?

Japan 28no.