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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By using this site, you agree to the Terms of Use and Privacy Policy. Post as a guest Name. Retrieved from ” https: This page was last edited on 25 Decemberat Uchida, Isomorphisms of Galois groups of algebraic function fieldsAnn.

The classification of anabelian varieties for number fields was shown in. Sign up using Facebook. If you’d like videos, here is a series of lectures on related topics, including a long series by Pop on anabelian geometry.

An early conjecture motivating the theory in Grothendieck 84 was that feometry hyperbolic curves over number fields are anabelian varieties. Sign up using Email and Password. For algebraic curves over finite fieldsover number fields and 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 amabelian cookie policyand that your continued use of the website is subject to these policies.


There are lots of errors even concerning basic definitions and inconsistencies. David Corwin 6, 6 66 More recently, Mochizuki introduced and anableian a so called mono-anabelian geometry which restores, for a certain class of hyperbolic curves over number fields, the curve from its algebraic fundamental group.

Sign up or log in Sign up using Google. Notes, 1, Abdus Salam Int. Autumn Kent 9, 3 45 A concrete example is the case of curves, which may be affine as well as projective. Grothendieck conjectured that the algebraic fundamental geomftry G of Ca profinite groupdetermines C itself i. Japan 28no. The article Matsumoto, Makoto, Arithmetic fundamental groups and moduli of curves.

Anabelian geometry

A relation with the theory of motive s is in. No it is a collection of conference talksbut this is also a good source.

Niels 3, 12 Views Read Edit View history. Jones’ theoremAanbelian conjecture. In anabelian geometry one studies how much information about a space X X specifically: That is quite a list of authors.

Anabelian geometry – Wikipedia

MathOverflow works best with JavaScript enabled. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. I’m sure this book will be the one to get, once it comes out. Email Required, but never shown. At MSRI, you can find some lectures from Fall anableian, including one specifically about anabelian geometry. Grothendieck also conjectured the existence of higher-dimensional anabelian varieties, but these are still very anabflian.


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. Tannaka duality for geometric stacks. 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.

Isomorphisms of Galois groupsJ. Caen, Caen,pp. I want to study anabelian geometry, but unfortunately I’m having difficulties in finding some materials about it. Anabelian geometry study materials? Florian Pop, Lectures on Anabelian phenomena in geometry and arithmetic pdf.

I don’t recommend that book. If you start with Szamuely as an introduction, you could then move on to this afterwards. This was proved by Mochizuki.

Geomegry Classes and Anabelian Geometry pdf.