Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0673.14001
Beckmann, Sybilla
Galois groups of fields of definition of solvable branched coverings. (English)
[J] Compos. Math. 66, No.2, 121-144 (1988). ISSN 0010-437X; ISSN 1570-5846/e

Assume one is given a solvable branched covering $X\to P\sp 1$ with Galois group G, let K be a field of definition of this covering and let $H=gal(K/{\bbfQ})$. The problem adressed to is: give information on H in terms of G for a suitable ``small'' K. The main theorem of the present paper shows that given a topological description of this covering (i.e. a family of elements in G corresponding to a standard homotopy basis of $P\sp 1\setminus discri\min ant)$ and ``knowing'' a chief series of G (i.e. a series $G\sb m\subset G\sb{m-1}\subset...\subset G\sb 0=G$ with $G\sb{i+1}$ normal in $G\sb i$ and $G\sb{i+1}$ maximal among normal subgroups of G contained in $G\sb i)$ one can describe the factor groups $H\sb j/H\sb{j+1}$ of a subinvariant series $H\sb n\triangleleft H\sb{n- 1}\triangleleft...\triangleleft H\sb 0=H$ for a suitable K. In particular it follows that if L is the field of definition for the branch points of the covering and M is the Galois closure over L of the field of moduli of the covering then gal(M/L) is an extension of abelian groups and subquotients of symplectic groups.
[A.Buium]

MSC 2000:: *14A05 Relevant commutative algebra
14E20 Coverings, fundamental group (mappings)
14H10 Families, algebraic moduli (curves)
14H30 Coverings, fundamental group (curves)

Keywords: small field of definition; solvable branched covering

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]