Talk:Severi–Brauer variety

Is there a particular reason this is not called a Brauer-Severi variety, as per the mathematical convention of giving credit in alphabetical order?

For example, that's what the book of Görtz and Wedhorn (Algebraic Geometry I) calls them.

What is the field of definition of the degree d embedding?
Is the second sentence in the following correct?

"As a consequence, we see that if the class of X has order d in the Brauer group then there is a divisor class of degree d on X. The associated linear system defines the d-dimensional embedding of X over a splitting field L."

I thought that Pic(X) in the exact sequence is Pic(X/K), so the conclusion should be

"The associated linear system defines a d-dimensional embedding of X over the field K."

JosephSilverman (talk) 14:06, 22 January 2018 (UTC)

Article improvements
This article could be improved by Kaptain-k-theory (talk) 21:34, 8 April 2021 (UTC)
 * giving detailed examples outlined in http://web.archive.org/web/20210124143859/https://mcfaddin.github.io/documents/MockAMSTalk2014.pdf
 * Stating theorem 1.6.6 in https://people.math.rochester.edu/faculty/doug/otherpapers/Kbook.pdf
 * Relation to Galois cohomology - https://link.springer.com/article/10.1007/BF01357435