# Tag:Azumaya

• ## M-geometry (3)

For any finite dimensional A-representation S we defined before a character $\chi(S)$ which is an linear functional on the noncommutative functions $\mathfrak{g}_A = A/[A,A]_{vect}$ and defined via $\chi_a(S) = Tr(a | S)$ for all $a \in A$ We would like to have enough such characters to separate simples, that is we […]

• ## neverendingbooks-geometry (2)

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

• ## noncommutative curves and their maniflds

Last time we have seen that the noncommutative manifold of a Riemann surface can be viewed as that Riemann surface together with a loop in each point. The extra loop-structure tells us that all finite dimensional representations of the coordinate ring can be found by separating over points and those living at just one point…

• ## TheLibrary (demo)

It is far from finished but you can already visit a demo-version of TheLibrary which I hope will one day be a useful collection of online courses and books on non-commutative algebra & geometry. At the moment it just contains a few of my own things but I do hope that others will find the…

• ## Jacobian update

One way to increase the blogshare-value of this site might be to give readers more of what they want. In fact, there is an excellent guide for those who really want to increase traffic on their site called 26 Steps to 15k a Day. A somewhat sobering suggestion is rule S : “Think about what…

[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…