Applications of versal deformations to Galois theory | Zendy

Frauke M. Bleher | Zendy; Ted Chinburg | Zendy

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Applications of versal deformations to Galois theory

Author(s) -

Frauke M. Bleher,

Ted Chinburg

Publication year - 2003

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140300002

Subject(s) - endomorphism , mathematics , embedding , algebraically closed field , scalar (mathematics) , pure mathematics , block (permutation group theory) , representation (politics) , galois module , embedding problem , group (periodic table) , deformation (meteorology) , algebra over a field , galois theory , galois group , combinatorics , geometry , computer science , chemistry , physics , organic chemistry , artificial intelligence , politics , meteorology , political science , law

. In this paper we study which solutions to an embedding problem can be constructed using a versal deformation of a group representation over an algebraically closed field of positive characteristic. This question reduces (at least stably) to finding which representations of finite groups have faithful versal deformations. We determine exactly when a versal deformation of a representation of a finite group is faithful in case the representation belongs to a cyclic block and its endomorphisms are given by scalar multiplications.

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