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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Autumn Kent 9, 3 45 This was eventually proven by various authors in various cases. This volumeGalois Groups and Fundamental Groupsedited by Leila Schneps has a great collection of articles, as does this volumeGeometric Galois Actionsincluding a nice article by Florian Pop on “Glimpses of Grothendieck’s anabelian geometry.
An early conjecture motivating the theory in Grothendieck 84 was that all hyperbolic curves over number fields are anabelian varieties.
I’m sure this book will be the one to get, once it comes out. Japan 28no. There are lots of errors even concerning basic definitions and inconsistencies. Home Questions Tags Users Unanswered. The article Matsumoto, Makoto, Arithmetic fundamental groups and moduli of curves. Views Read Edit View history.
Yuri Tschinkel, Introduction to anabelian geometrytalk at Symmetries and correspondences in number theory, geometry, algebra, physics: Caen, Caen,pp. This was proved by Mochizuki. Kummer Classes and Anabelian Geometry pdf.
Geometfy Required, but never shown. Uchida, Isomorphisms of Galois groups of algebraic function fieldsAnn. For algebraic curves over finite fieldsover number fields and over p-adic field the statement was eventually completed by Mochizuki These Grothendieck conjectures were partially solved by Hiroaki Nakamura and Akio Tamagawa, while complete proofs were given by Shinichi Mochizuki.
Tannaka duality for geometric stacks.
A relation with the theory of motive s is in. Jones’ theoremDeligne-Kontsevich conjecture.
In anabelian geometry one studies how much information about a space X X specifically: Post as a guest Name. 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 – Wikipedia
This page was last edited on 25 Decemberat Sign up or log in Sign up using Google. 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 geoketry from its algebraic fundamental group.
I want to study anabelian geometry, but unfortunately I’m having difficulties in finding some materials geomefry it. Key results of mono-anabelian geometry were published in Mochizuki’s “Topics in Absolute Anabelian Geometry. Notes, 1, Abdus Salam Int. Suppose given a hyperbolic curve Ci. If you’d like videos, here is a series of lectures on related topics, including a long series by Pop on 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: Anabelian geometry study materials? Isomorphisms ansbelian Galois groupsJ.
Florian Pop, Lectures on Anabelian phenomena in geometry and arithmetic pdf. No it is a collection of conference talksbut this is also a good source. If you start with Szamuely as an introduction, you could then move on to this afterwards. Sign up using Facebook. A concrete example is the case of curves, which may be affine as well as projective.
Frans Oort, Lecture notes. The book mentioned by Felipe is available here: In Uchida and Neukirch it was shown that an isomorphism between Galois groups of number fields implies the existence of an isomorphism between those anableian fields.
The classification of anabekian varieties for number fields was shown in.