Specializations of Brauer classes over algebraic function fields

Authors:
Burton Fein and Murray Schacher

Journal:
Trans. Amer. Math. Soc. **352** (2000), 4355-4369

MSC (2000):
Primary 12E15, 12G05, 16K50

DOI:
https://doi.org/10.1090/S0002-9947-00-02474-0

Published electronically:
May 12, 2000

MathSciNet review:
1661250

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be either a number field or a field finitely generated of transcendence degree over a Hilbertian field of characteristic 0, let be the rational function field in one variable over , and let . It is known that there exist infinitely many such that the specialization induces a specialization , where has exponent equal to that of . Now let be a finite extension of and let . We give sufficient conditions on and for there to exist infinitely many such that the specialization has an extension to inducing a specialization , the residue field of , where has exponent equal to that of . We also give examples to show that, in general, such need not exist.

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Additional Information

**Burton Fein**

Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331

Email:
fein@math.orst.edu

**Murray Schacher**

Affiliation:
Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90024

Email:
mms@math.ucla.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02474-0

Keywords:
Brauer group,
Brauer-Hilbertian,
corestriction,
Hilbertian,
specializations.

Received by editor(s):
March 23, 1998

Received by editor(s) in revised form:
October 30, 1998

Published electronically:
May 12, 2000

Additional Notes:
The authors are grateful for support under NSA Grants MDA904-97-1-0040 and MDA904-97-1-0060, respectively.

Article copyright:
© Copyright 2000
American Mathematical Society