Relative Brauer groups in characteristic 𝑝

Aravire, Roberto; Jacob, Bill

doi:10.1090/S0002-9939-08-09746-3

Relative Brauer groups in characteristic $p$
HTML articles powered by AMS MathViewer

by Roberto Aravire and Bill Jacob PDF

Proc. Amer. Math. Soc. 137 (2009), 1265-1273 Request permission

Abstract:

This paper gives a description of the relative Brauer group $\textrm {Br}(E/F)$ when $F$ has characteristic $p$, $[E:F]=p$, and the Galois group $\textrm {Gal}(E_1/F)$ is solvable, where $E_1$ is the Galois closure of $E$ over $F$.

References

A. A. Albert, A note on normal division algebras of prime degree, Bull. Amer. Math. Soc. 44 (1938), no. 10, 649–652. MR 1563842, DOI 10.1090/S0002-9904-1938-06831-0
Jón Kr. Arason, R. Aravire, and R. Baeza, On some invariants of fields of characteristic $p>0$, J. Algebra 311 (2007), no. 2, 714–735. MR 2314731, DOI 10.1016/j.jalgebra.2007.02.037
Emil Artin, Galois theory, Notre Dame Mathematical Lectures, no. 2, University of Notre Dame Press, South Bend, Ind., 1959. Edited and supplemented with a section on applications by Arthur N. Milgram; Second edition, with additions and revisions; Fifth reprinting. MR 0265324
Spencer Bloch and Kazuya Kato, $p$-adic étale cohomology, Inst. Hautes Études Sci. Publ. Math. 63 (1986), 107–152. MR 849653, DOI 10.1007/BF02831624
Pascal Mammone and Jean-Pierre Tignol, Dihedral algebras are cyclic, Proc. Amer. Math. Soc. 101 (1987), no. 2, 217–218. MR 902530, DOI 10.1090/S0002-9939-1987-0902530-6
I. Reiner, Maximal orders, London Mathematical Society Monographs, No. 5, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1975. MR 0393100
Louis H. Rowen and David J. Saltman, Dihedral algebras are cyclic, Proc. Amer. Math. Soc. 84 (1982), no. 2, 162–164. MR 637160, DOI 10.1090/S0002-9939-1982-0637160-2
Ernst Witt, $p$-Algebren und Pfaffsche Formen, Abh. Math. Sem. Univ. Hamburg 22 (1958), 308–315 (German). MR 97377, DOI 10.1007/BF02941961