Displaying similar documents to “On the depth of the relations of the maximal unramified pro-p Galois group over the cyclotomic ℤₚ-extension”

On the inverse problem of Galois theory.

Núria Vila (1992)

Publicacions Matemàtiques

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The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in the recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.

On double covers of the generalized alternating group ℤ d ≀ m as Galois groups over algebraic number fields

Martin Epkenhans (1997)

Acta Arithmetica

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Let ℤ d ≀ m b e t h e g e n e r a l i z e d a l t e r n a t i n g g r o u p . W e p r o v e t h a t a l l d o u b l e c o v e r s o f ℤd ≀ m o c c u r a s G a l o i s g r o u p s o v e r a n y a l g e b r a i c n u m b e r f i e l d . W e f u r t h e r r e a l i z e s o m e o f t h e s e d o u b l e c o v e r s a s t h e G a l o i s g r o u p s o f r e g u l a r e x t e n s i o n s o f ℚ ( T ) . I f d i s o d d a n d m > 7 , t h e n e v e r y c e n t r a l e x t e n s i o n o f ℤd ≀ m o c c u r s a s t h e G a l o i s g r o u p o f a r e g u l a r e x t e n s i o n o f ℚ ( T ) . W e f u r t h e r i m p r o v e s o m e o f o u r e a r l i e r r e s u l t s c o n c e r n i n g d o u b l e c o v e r s o f t h e g e n e r a l i z e d s y m m e t r i c g r o u p ℤd ≀ m .

On cohomological systems of Galois representations

Wojciech Gajda, Sebastian Petersen (2016)

Banach Center Publications

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The paper contains an expanded version of the talk delivered by the first author during the conference ALANT3 in Będlewo in June 2014. We survey recent results on independence of systems of Galois representations attached to ℓ-adic cohomology of schemes. Some other topics ranging from the Mumford-Tate conjecture and the Geyer-Jarden conjecture to applications of geometric class field theory are also considered. In addition, we have highlighted a variety of open questions which can lead...