Absolute anabelian cuspidalizations of proper hyperbolic curves
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In this paper, the authors develop the theory ofcuspidalizations of the etale fundamental group of a proper hyperbolic curve over a finite or nonarchimedean mixed-characteristic local field.Abstract:
In this paper, we develop the theory of “cuspidalizations” of the etale fundamental group of a proper hyperbolic curve over a finite or nonarchimedean mixed-characteristic local field. The ultimate goal of this theory is the group-theoretic reconstruction of the etale fundamental group of an arbitrary open subscheme of the curve from the etale fundamental group of the full proper curve. We then apply this theory to show that a certain absolute $p$-adic version of the Grothendieck Conjecture holds for hyperbolic curves “of Belyi type”. This includes, in particular, affine hyperbolic curves over a nonarchimedean mixed-characteristic local field which are defined over a number field and isogenous to a hyperbolic curve of genus zero. Also, we apply this theory to prove the analogue for proper hyperbolic curves over finite fields of the version of the Grothendieck Conjecture that was shown in [Tama].read more
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Book ChapterDOI
Lie Algebras and Lie Groups
William Fulton,Joe Harris +1 more
TL;DR: In this article, the Campbell-Hausdorff formula is used to establish the First and Second Principles of §8.1 below; if you are willing to take those on faith the formula and exercises dealing with it can be skimmed.
Journal Article
Topics in Absolute Anabelian Geometry I: Generalities
TL;DR: The first part of a three-part series on absolute anabelian geometry can be found in this paper, where the authors consider the problem of computing the quotient of an arithmetic fundamental group determined by the absolute Galois group of the base field.
Journal ArticleDOI
On the combinatorial anabelian geometry of nodally nondegenerate outer representations
TL;DR: In this paper, a generalization of this result to the case of proper hyperbolic curves has been obtained, where the dimension of the configuration space is reduced from two to one and the inner automorphisms of the fundamental group of a configuration space associated to a hyper-bolic curve are obtained.
Journal Article
Topics in absolute anabelian geometry iii: global reconstruction algorithms
TL;DR: In this paper, the authors apply the ab- solute anabelian technique of Belyi cuspidalization developed in the second part, together with certain ideas contained in an earlier paper of the author concerning the category-theoretic representation of holomorphic structures via either the topologi- cal group SL2(R) or the use of "parallelograms, rectangles, and squares", to develop a certain global formalism for certain hyperbolic orbicurves related to a once- punctured elliptic curve over a number field.
References
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Journal ArticleDOI
The irreducibility of the space of curves of given genus
Pierre Deligne,David Mumford +1 more
TL;DR: In this article, the authors implique l'accord avec les conditions generales d'utilisation (http://www.numdam.org/legal.php).
Book
Lie groups and Lie algebras
TL;DR: Seligman as mentioned in this paper presents a rich and useful volume of material beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or "Tits systems".
Book
Cohomology of number fields
TL;DR: Part I algebraic theory: Cohomology of Profinite groups as mentioned in this paper, some homological algebra, duality properties of profinite groups, free products of finite groups, Iwasawa Modules.