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

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 Computation of Galois groups over function fields

1997 ◽  
Vol 66 (218) ◽  
pp. 823-832 ◽  
Author(s):  
Thomas Mattman ◽  
John McKay
Keyword(s):  
Function Fields ◽  
Galois Groups

scholarly journals Non-abelian Cohen–Lenstra heuristics over function fields

2017 ◽  
Vol 153 (7) ◽  
pp. 1372-1390 ◽  
Author(s):  
Nigel Boston ◽  
Melanie Matchett Wood
Keyword(s):  
Function Fields ◽  
Quadratic Function ◽  
Number Fields ◽  
Galois Groups ◽  
Quadratic Number ◽  
Quadratic Extensions ◽  
Quadratic Number Fields ◽  
Imaginary Quadratic Number ◽  
Unique Distribution ◽  
Quadratic Function Fields

Boston, Bush and Hajir have developed heuristics, extending the Cohen–Lenstra heuristics, that conjecture the distribution of the Galois groups of the maximal unramified pro-$p$extensions of imaginary quadratic number fields for$p$an odd prime. In this paper, we find the moments of their proposed distribution, and further prove there is a unique distribution with those moments. Further, we show that in the function field analog, for imaginary quadratic extensions of$\mathbb{F}_{q}(t)$, the Galois groups of the maximal unramified pro-$p$extensions, as$q\rightarrow \infty$, have the moments predicted by the Boston, Bush and Hajir heuristics. In fact, we determine the moments of the Galois groups of the maximal unramified pro-odd extensions of imaginary quadratic function fields, leading to a conjecture on Galois groups of the maximal unramified pro-odd extensions of imaginary quadratic number fields.

scholarly journals Galois groups over function fields of positive characteristic

2010 ◽  
Vol 138 (04) ◽  
pp. 1205-1205 ◽  
Author(s):  
John Conway ◽  
John McKay ◽  
Allan Trojan
Keyword(s):  
Positive Characteristic ◽  
Function Fields ◽  
Galois Groups
Sign in / Sign up

Export Citation Format

Share Document