Finitely generated pro-p-groups as Galois groups of maximalp-extensions of function fields over ℚ q

1996 ◽  
Vol 90 (1) ◽  
pp. 225-238 ◽  
Author(s):  
Christian U. Jensen ◽  
Alexander Prestel
Keyword(s):  
Function Fields ◽  
Galois Groups ◽  
Finitely Generated

Fields of definition of function fields and hurwitz families — groups as galois groups

1977 ◽  
Vol 5 (1) ◽  
pp. 17-82 ◽  
Author(s):  
M. Fried
Keyword(s):  
Function Fields ◽  
Galois Groups ◽  
Definition Of

scholarly journals FINITE GROUPS AS GALOIS GROUPS OF FUNCTION FIELDS WITH INFINITE FIELD OF CONSTANTS

2010 ◽  
Vol 88 (3) ◽  
pp. 301-312
Author(s):  
C. ÁLVAREZ-GARCÍA ◽  
G. VILLA-SALVADOR
Keyword(s):  
Finite Groups ◽  
Function Field ◽  
Function Fields ◽  
Galois Groups ◽  
Infinite Field ◽  
Separable Extension ◽  
Separable Extensions

AbstractLetE/kbe a function field over an infinite field of constants. Assume thatE/k(x) is a separable extension of degree greater than one such that there exists a place of degree one ofk(x) ramified inE. LetK/kbe a function field. We prove that there exist infinitely many nonisomorphic separable extensionsL/Ksuch that [L:K]=[E:k(x)] andAutkL=AutKL≅Autk(x)E.

scholarly journals Finite presentability of arithmetic groups over global function fields

1987 ◽  
Vol 30 (1) ◽  
pp. 23-39 ◽  
Author(s):  
Helmut Behr
Keyword(s):  
Small Groups ◽  
Function Fields ◽  
Algebraic Groups ◽  
Number Fields ◽  
Arithmetic Groups ◽  
Finitely Generated ◽  
Global Function ◽  
Global Function Fields ◽  
Finite Presentability ◽  
Finitely Presented

Arithmetic subgroups of reductive algebraic groups over number fields are finitely presentable, but over global function fields this is not always true. All known exceptions are “small” groups, which means that either the rank of the algebraic group or the set S of the underlying S-arithmetic ring has to be small. There exists now a complete list of all such groups which are not finitely generated, whereas we onlyhave a conjecture which groups are finitely generated but not finitely presented.

scholarly journals On residually transcendental valued function fields of conics

1996 ◽  
Vol 38 (2) ◽  
pp. 137-145
Author(s):  
Sudesh K. Khanduja
Keyword(s):  
Valuation Ring ◽  
Function Fields ◽  
Residue Field ◽  
Field Extension ◽  
Transcendence Degree ◽  
Finitely Generated ◽  
Uniqueness Property ◽  
Transcendental Extension

Let K/Kobe a finitely generated field extension of transcendence degree 1. Let u0 be a valuation of Koand v a valuation of Kextending v0such that the residue field of vis a transcendental extension ofthe residue field k0of vo/such a prolongation vwill be called a residually transcendental prolongation of v0. Byan element with the uniqueness propertyfor (K, v)/(K0, v0) (or more briefly for v/v0)we mean an element / of Khaving u-valuation 0 which satisfies (i) the image of tunder the canonicalhomomorphism from the valuation ring of vonto the residue field of v(henceforth referred to as the v-residue ot t) is transcendental over ko; that is vcoincides with the Gaussian valuation on the subfield K0(t) defined by (ii) vis the only valuation of K (up to equivalence) extending the valuation .

scholarly journals Finitely Generated Pro-pAbsolute Galois Groups over Global Fields

1999 ◽  
Vol 77 (1) ◽  
pp. 83-96 ◽  
Author(s):  
Ido Efrat
Keyword(s):  
Galois Groups ◽  
Finitely Generated ◽  
Global Fields

scholarly journals Finitely generated pro-p Galois groups of p-Henselian fields

1999 ◽  
Vol 138 (3) ◽  
pp. 215-228 ◽  
Author(s):  
Ido Efrat
Keyword(s):  
Galois Groups ◽  
Finitely Generated

The Mordel-Weil theorems for Drinfeld modules over finitely generated function fields

2001 ◽  
Vol 106 (3) ◽  
pp. 305-314 ◽  
Author(s):  
Julie Tzu-Yueh Wang
Keyword(s):  
Function Fields ◽  
Drinfeld Modules ◽  
Finitely Generated

scholarly journals Reconstructing function fields from rational quotients of mod- $$\ell $$ ℓ Galois groups

2015 ◽  
Vol 366 (1-2) ◽  
pp. 337-385 ◽  
Author(s):  
Adam Topaz
Keyword(s):  
Function Fields ◽  
Galois Groups
Sign in / Sign up

Export Citation Format

Share Document