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.
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.
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.
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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?