Hodge‐Theoretic Obstruction to the Existence of Quaternion Algebras | Zendy

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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.

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