First page Abstract In the present paper, we study the anabelian geometry of mixedcharacteristic local fields by an algorithmic approach. We begin by discussing some generalities on log-shells of mixed-characteristic local fields. One main topic of this discussion is the difference between the log-shell and the ring of integers. Next, we consider open homomorphisms between profinite groups of MLF-type. This consideration leads us to a bi-anabelian result for absolutely unramified mixed-characteristic local fields. Next, we establish some mono-anabelian reconstruction algorithms related to each of absolutely abelian mixed-characteristic local fields, mixed-characteristic local fields of degree one, and Galois-specifiable mixed-characteristic local fields.
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That is quite a list of authors. Anabelian geometry 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.
David Corwin 6, 6 66 Anabelian geometry study materials? 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.
Sign up using Email and Password. 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: This was proved by Mochizuki.
Anabelian geometry — Wikipedia Niels 3, 12 The book mentioned by Felipe is available here: An early conjecture motivating the theory in Grothendieck 84 was that all hyperbolic curves over number fields are anabelian varieties. A concrete example is the case of curves, which may be affine as well as projective.
Florian Pop, Lectures on Anabelian phenomena in geometry geometdy arithmetic pdf. Post as a guest Name. Views Read Edit View history. Kummer Classes and Anabelian Geometry pdf.
For algebraic curves over finite fieldsover number fields and over p-adic field the statement was eventually completed by Mochizuki Suppose given a hyperbolic curve Ci. From Wikipedia, the free encyclopedia. Grothendieck conjectured that the algebraic fundamental group G of Ca profinite groupdetermines C itself i. Frans Oort, Geomerty notes. This page was last edited on 25 Decemberat Sign anaabelian or log in Sign up using Google.
If you start with Szamuely as an introduction, you could then move on to this afterwards. Grothendieck also conjectured the existence of higher-dimensional anabelian varieties, but these are still very mysterious. Isomorphisms of Galois groupsJ. Notes, 1, Abdus Salam Int. Yuri Tschinkel, Introduction to anabelian geometrytalk at Symmetries and correspondences in number theory, geometry, algebra, physics: Caen, Caen,pp.
Annabelian up using Facebook. No it is a collection of conference talksbut this is also a good source. A relation with the theory of motive s is in. The classification of anabelian varieties for number fields was shown in. These Grothendieck conjectures were partially solved by Hiroaki Nakamura and Akio Tamagawa, while complete proofs were given by Shinichi Mochizuki. The article Matsumoto, Makoto, Arithmetic fundamental groups and moduli of curves. Yuri TschinkelIntroduction to anabelian geometrytalk at Symmetries and correspondences in number theory, geometry, algebra, physics: Uchida, Isomorphisms of Galois groups of algebraic function fieldsAnn.
There are lots of errors even concerning basic definitions and inconsistencies. Home Questions Tags Users Unanswered. This was eventually proven by various authors in various cases. Most Related.
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