Galois action on knots I: Action of the 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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It is well known that the Galois group of an extension L/F puts constraints on the structure of the relative ideal class group Cl(L/F ). Explicit results, however, hardly ever go beyond the semisimple abelian case, where L/F is abelian (in general cyclic) and where (L : F ) and #Cl(L/F ) are coprime. Using only basic parts of the theory of group representations, we give a unified approach to th...
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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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A geometric interpretation and generalisation for the Galois action on finite group character tables is sketched.
متن کاملThe action of the Galois Group on the Torsion-free part of Unit Group in a Totally Complex Galois Extension over Q with Galois Group S3
This is the senior thesis I worked on in University of Washington, under the supervision of Prof. Ralph Greenberg. We intended to classify the torsion-free part of the unit group of a totally complex normal extension with Galois group S3 as a Z[S3]-module. We obtained a way to recognize the module structure based on the class numbers of the field extensions. Conversely we also showed that some ...
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ژورنال
عنوان ژورنال: Quantum Topology
سال: 2017
ISSN: 1663-487X
DOI: 10.4171/qt/91