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ISRAEL JOURNAL OF MATHEMATICS 131 (2002), 375-379 FIELDS FOR WHICH THE PROJECTIVE SCHUR
 

Summary: ISRAEL JOURNAL OF MATHEMATICS 131 (2002), 375-379
FIELDS FOR WHICH THE PROJECTIVE SCHUR
SUBGROUP IS THE WHOLE BRAUER GROUP
BY
ELI ALJADEFF AND JACK SONN
Department of Mathematics, Technion -- Israel Institute of Technology
Haifa 32000, Israel
e-mail: aljadeff@math.technion.ac.il, sonn@math.technion.ac.il
ABSTRACT
Let Br(K) denote the Brauer group of a field K and PS(K) the
projective Sehur subgroup.
i. Let K be a finitely generated infinite field. Then PS(K) =Br(K)
if and only if I( is a global field.
2. Let /x~ be a finitely generated infinite field, and let K((t)) denote
the field of formal power series in t over /iv. Then P S ( K ( ( t ) ) ) ---
Br(K((t))) if and only if K = Q.
1. Introduction
Let K be any field. The projective Schur (sub)group PS(K) of a field K is
the subgroup of the Brauer group Br(K) generated by (in fact, consisting of) all
classes that are represented by a projective Schur algebra A. A finite dimensional

  

Source: Aljadeff, Eli - Department of Mathematics, Technion, Israel Institute of Technology

 

Collections: Mathematics