# Tag:Brauer-Severi

• ## neverendingbooks-geometry (2)

Here pdf-files of older NeverEndingBooks-posts on geometry. For more recent posts go here.

• ## down with determinants

The categorical cafe has a guest post by Tom Leinster Linear Algebra Done Right on the book with the same title by Sheldon Axler. I haven’t read the book but glanced through his online paper Down with determinants!. Here is ‘his’ proof of the fact that any n by n matrix A has at least…

• ## lulu neverendingbooks

Half a year ago, it all started with NeverEndingBooks in which I set out a rather modest goal : Why NeverEndingBooks ? We all complain about exaggerated prices of mathematical books from certain publishers, poor quality of editing and refereeing offered, as well as far too stringent book-contracts. Rather than lamenting about this, NeverEndingBooks gives…

One of the things I like most about returning from a vacation is to have an enormous pile of fresh reading : a week's worth of newspapers, some regular mail and much more email (three quarters junk). Also before getting into bed after the ride I like to browse through the arXiv in search for…

• ## hyper-resolutions

[Last time][1] we saw that for $A$ a smooth order with center $R$ the Brauer-Severi variety $X_A$ is a smooth variety and we have a projective morphism $X_A \rightarrow \mathbf{max}~R$ This situation is very similar to that of a desingularization $~X \rightarrow \mathbf{max}~R$ of the (possibly singular) variety $~\mathbf{max}~R$. The top variety $~X$ is a…

• ## smooth Brauer-Severis

Around the same time Michel Van den Bergh introduced his Brauer-Severi schemes, [Claudio Procesi][1] (extending earlier work of [Bill Schelter][2]) introduced smooth orders as those orders $A$ in a central simple algebra $\Sigma$ (of dimension $n^2$) such that their representation variety $\mathbf{trep}_n~A$ is a smooth variety. Many interesting orders are smooth : hereditary orders, trace…

• ## Brauer-Severi varieties

![][1] Classical Brauer-Severi varieties can be described either as twisted forms of projective space (Severi\’s way) or as varieties containing splitting information about central simple algebras (Brauer\’s way). If $K$ is a field with separable closure $\overline{K}$, the first approach asks for projective varieties $X$ defined over $K$ such that over the separable closure \$X(\overline{K})…