Tensor products of division algebras and fields

Louis Rowen; David J. Saltman

doi:10.1016/j.jalgebra.2013.07.019

Tensor products of division algebras and fields

Louis Rowen
, David J. Saltman

Department of Mathematics

Institute for Defense Analyses

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

This paper began as an investigation of the question of whether D₁⊗_FD₂ is a domain where the D_i 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 F_i 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
Pages (from-to)	296-309
Number of pages	14
Journal	Journal of Algebra
Volume	394
DOIs	https://doi.org/10.1016/j.jalgebra.2013.07.019
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
United States-Israel Binational Science Foundation	2010149

Keywords

Brauer group
Division algebra
Picard group
Ramification
Schur index

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10.1016/j.jalgebra.2013.07.019

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AU - Saltman, David J.

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AB - 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.

KW - Brauer group

KW - Division algebra

KW - Picard group

KW - Ramification

KW - Schur index

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VL - 394

SP - 296

EP - 309

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Tensor products of division algebras and fields

Abstract

Bibliographical note

Funding

Keywords

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