Quartic exercises.

Knus, Max-Albert; Tignol, Jean-Pierre

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Severi-Brauer varieties of semidirect product algebras.

Krashen, Daniel (2003)

Documenta Mathematica

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Central extensions of reductive groups by $K_{2}$

Jean-Luc Brylinski, Pierre Deligne (2001)

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Galois groups of fields of definition of solvable branched coverings

Sybilla Beckmann (1988)

Compositio Mathematica

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On Galois cohomology and realizability of 2-groups as Galois groups

Ivo Michailov (2011)

Open Mathematics

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In this paper we develop some new theoretical criteria for the realizability of p-groups as Galois groups over arbitrary fields. We provide necessary and sufficient conditions for the realizability of 14 of the 22 non-abelian 2-groups having a cyclic subgroup of index 4 that are not direct products of groups.

Recent work on differential Galois theory

Marius Van der Put (1997-1998)

Séminaire Bourbaki

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Characteres and Galois invariants of regular dessins.

Manfred Streit, Jürgen Wolfart (2000)

Revista Matemática Complutense

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We describe a new invariant for the action of the absolute Galois groups on the set of Grothendieck dessins. It uses the fact that the automorphism groups of regular dessins are isomorphic to automorphism groups of the corresponding Riemman surfaces and define linear represenatations of the space of holomorphic differentials. The characters of these representations give more precise information about the action of the Galois group than all previously known invariants, as it is shown...

CM points and quaternion algebras.

Cornut, C., Vatsal, V. (2005)

Documenta Mathematica

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On Galois cohomology and realizability of 2-groups as Galois groups II

Ivo Michailov (2011)

Open Mathematics

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In [Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 403–419] we calculated the obstructions to the realizability as Galois groups of 14 non-abelian groups of order 2n, n ≥ 4, having a cyclic subgroup of order 2n−2, over fields containing a primitive 2n−3th root of unity. In the present paper we obtain necessary and sufficient conditions for the realizability of the remaining 8 groups that are not direct products of...

Rational connectedness and Galois covers of the projective line.

Colliot-Thélène, Jean-Louis (2000)

Annals of Mathematics. Second Series

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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 $.$

Effective lifting of 2-cocycles for Galois cohomology

Thomas Preu (2013)

Open Mathematics

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We give explicit formulas for reducing the problem of determining whether a given 2-cocycle is a coboundary and if so finding a lifting 1-cochain to a system of norm equations.