Speaker:* Thomas Polstra, University of Virginia, Charlottesville, VA, USA*
Date/Time: *19 March 2021, 6:30pm IST/ 1:00pm GMT / 9:00am EDT* (joining
time 6:15pm IST).
Google meet link:
https://meet.google.com/ujr-hykc-cjm
Title:* Prime characteristic singularities and the deformation problem*
Abstract: Let $P$ be a property of local rings (such as regular,
Gorenstein, or complete). We say that $P$ deforms if a local ring $R$
enjoys property $P$ provided there exists a nonzerodivisor $x$ such that
$R/xR$ is $P$. (For example, the properties of being regular or Gorenstein
deform, but the property of being complete does not deform). The
deformation problem, as it pertains to the prime characteristic singularity
classes of $F$-regular, $F$-rational, $F$-pure, and $F$-injective
singularities, has a rich history that dates to work of Fedder in the
1980's and remains an active research area. We will survey the history of
the deformation problem of these four prime characteristic singularity
classes and discuss a recent solution to the deformation of $F$-purity
problem in rings which are $\mathbb{Q}$-Gorenstein. This talk is based on a
collaboration with Austyn Simpson.
For more information and links to previous seminars, visit the website of
VCAS:
https://sites.google.com/view/virtual-comm-algebra-seminar