Abstract
This paper began as an investigation of the question of whether D1⊗FD2 is a domain where the Di are division algebras and F is an algebraically closed field contained in their centers. We present an example where the answer is "no", and also study the Picard group and Brauer group properties of F1⊗FF2 where the Fi are fields. Finally, as part of our example, we have results about division algebras and Brauer groups over curves. Specifically, we give a splitting criterion for certain Brauer group elements on the product of two curves over F.
Original language | English |
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Pages (from-to) | 296-309 |
Number of pages | 14 |
Journal | Journal of Algebra |
Volume | 394 |
DOIs | |
State | Published - 5 Nov 2013 |
Bibliographical note
Funding Information:This work was supported by the U.S.–Israel BSF (grant no. 2010149 ).
Funding
This work was supported by the U.S.–Israel BSF (grant no. 2010149 ).
Funders | Funder number |
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United States-Israel Binational Science Foundation | 2010149 |
Keywords
- Brauer group
- Division algebra
- Picard group
- Ramification
- Schur index