The following are some fun side hustles.
Computing Brauer group on Projective Markoff surfaces
This is an expository note on a detailed computation of the Brauer group for the projective and affine Markoff surface, for the learning seminar on obstruction to rational points.
This is an expository note on a detailed computation of the Brauer group for the projective and affine Markoff surface, for the learning seminar on obstruction to rational points.
Torsors on Schemes
An expository note focused on torsors and the sheaf view. Unfortunately had to skip any mentioning of the diff-geo side (curvature and reduction of principal bundles). This is also for the learning seminar on obstruction to rational points.
An expository note focused on torsors and the sheaf view. Unfortunately had to skip any mentioning of the diff-geo side (curvature and reduction of principal bundles). This is also for the learning seminar on obstruction to rational points.
Verifying semi-smallness of the squaring map on the Borel subgroup of GL_n(C)
We verify that the squaring map $f \colon B \to B$ on the Borel subgroup is a semi-small affine morphism for $n \leq 5$. This would imply $Rf_* Q[n(n-1)/2]$ is a perverse sheaf on $B$.
We verify that the squaring map $f \colon B \to B$ on the Borel subgroup is a semi-small affine morphism for $n \leq 5$. This would imply $Rf_* Q[n(n-1)/2]$ is a perverse sheaf on $B$.