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Uniform distribution of Hasse invariants. (English) Zbl 0603.12008

Algebras of uniformly distributed Hasse invariants (which form a subgroup of the Brauer group, containing the Schur subgroup) are studied. Some properties of such algebras are given, mainly concerning primitive roots \(\epsilon\) of unity.
For example, the following result is established: if \(K_ 1\) and \(K_ 2\) are extensions of a number field F such that \(K_ 1K_ 2\) is normal over F, D is a division algebra over \(K_ 1\) with uniformly distributed Hasse invariants which has index m, and is \((n,K_ 2)\)-adequate, and if m is relatively prime to the index of \(K_ 1K_ 2\) in \(N_ 1K_ 2\), where \(N_ 1\) is the normal closure of \(K_ 1\), then \(\epsilon_{m/g}\) is in \(K_ 2\), where g is the g.c.d. of m and of the index of \(K_ 1\) in \(N_ 1\).
Reviewer: T.Spircu

MSC:

11R52 Quaternion and other division algebras: arithmetic, zeta functions
12E15 Skew fields, division rings
14F22 Brauer groups of schemes
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