منابع مشابه
Separated Belyi Maps
We construct Belyi maps having specified behavior at finitely many points. Specifically, for any curve C defined over Q, and any disjoint finite subsets S, T ⊂ C(Q), we construct a finite morphism φ : C → P such that φ ramifies at each point in S, the branch locus of φ is {0, 1,∞}, and φ(T ) ∩ {0, 1,∞} = ∅. This refines a result of Mochizuki’s. We also prove an analogous result over fields of p...
متن کاملNoncritical Belyi Maps
×ØÖÖغ In the present paper, we present a slightly strengthened version of a well-known theorem of Belyi on the existence of " Belyi maps ". Roughly speaking, this strengthened version asserts that there exist Belyi maps which are unramified at [cf. Theorem 2.5] — or even near [cf. Corollary 3.2] — a prescribed finite set of points. Write C for the complex number field; Q ⊆ C for the subfield o...
متن کاملBelyi-extending Maps and the Galois Action on Dessins D’enfants
We study the absolute Galois group by looking for invariants and orbits of its faithful action on Grothendieck’s dessins d’enfants. We define a class of functions called Belyi-extending maps, which we use to construct new Galois invariants of dessins from previously known invariants. Belyiextending maps are the source of the “new-type” relations on the injection of the absolute Galois group int...
متن کاملBelyi-extending Maps and the Galois Action on ̂π1(p 1 C \ {0, 1, ∞})
We study the action of the absolute Galois group Gal(Q̄/Q) on the algebraic fundamental group of P1C\{0, 1,∞}. We define a class of functions called Belyi-extending maps, and using them we are able to (1) give new Galois invariants of Grothendieck’s dessins d’enfants and (2) give explicit relations on the fσ in terms of which the Galois action on π̂1(P 1 C \ {0, 1,∞}) is known.
متن کاملBelyi functions for Archimedean solids
Without doubt the authentic type of these gures exists in the mind of God the Creator and shares His eternity. Abstract The notion of a Belyi function is a main technical tool which relates the combinatorics of maps (i.e., graphs embedded into surfaces) with Galois theory, algebraic number theory, and the theory of Riemann surfaces. In this paper we compute Belyi functions for a class of semi-r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2014
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2014.v21.n6.a10