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Hodge‐Theoretic Obstruction to the Existence of Quaternion Algebras
Author(s) -
Kresch Andrew
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001546
Subject(s) - mathematics , quaternion , pure mathematics , brauer group , torsion (gastropod) , hodge theory , algebra over a field , quaternion algebra , field (mathematics) , division algebra , subalgebra , geometry , medicine , surgery , cohomology
This paper gives a necessary criterion in terms of Hodge theory for representability by quaternion algebras of certain 2‐torsion classes in the unramified Brauer group of a complex function field. This criterion is used to give examples of threefolds with unramified Brauer group elements which are the classes of biquaternion division algebras.