Fields with almost small absolute Galois group
نویسندگان
چکیده
منابع مشابه
About Absolute Galois Group
Absolute Galois Group defined as Galois group of algebraic numbers regarded as extension of rationals is very difficult concept to define. The goal of classical Langlands program is to understand the Galois group of algebraic numbers as algebraic extension of rationals Absolute Galois Group (AGG) through its representations. Invertible adeles -ideles define Gl1 which can be shown to be isomorph...
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We use elementary algebraic methods to reprove a theorem which was proved by Pop using rigid analytic geometry and in a less general form by Harbater using formal algebraic patching: Let C be an algebraically closed field of cardinality m. Consider a subset S of P(C) of cardinality m. Then the fundamental group of P(C) rS is isomorphic to the free profinite group of rank m. We also observe that...
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where A(co) stands for the discriminant of the complex lattice generated by 1 and to and g2(u) is the Weierstrass invariant of this lattice. If ti=Q(\/ — D) is an imaginary quadratic number field, it is well known from the theory of class fields with complex multiplication that the "singular values" j(a), where a£û, la >0, generate algebraic number fields which are abelian over fi, namely the s...
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A splitting field of a central simple algebra is said to be absolute Galois if it is Galois over some fixed subfield of the centre of the algebra. The paper proves an existence theorem for such fields over global fields with enough roots of unity. As an application, all twisted function fields and all twisted Laurent series rings over symbol algebras (or p-algebras) over global fields are cross...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2016
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-016-1356-z