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SUMMARY:Thomas Polstra (University of Virgina)
DTSTART:20210319T130000Z
DTEND:20210319T140000Z
DTSTAMP:20260423T021011Z
UID:VCAS/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/73/">Pr
 ime characteristic singularities and the deformation problem</a>\nby Thoma
 s Polstra (University of Virgina) as part of IIT Bombay Virtual Commutativ
 e Algebra Seminar\n\n\nAbstract\nLet $P$ be a property of local rings (suc
 h as regular\, Gorenstein\, or complete). We say that $P$ deforms if a loc
 al ring $R$ enjoys property $P$ provided there exists a nonzerodivisor $x$
  such that $R/xR$ is $P$. (For example\, the properties of being regular o
 r Gorenstein deform\, but the property of being complete does not deform).
  The deformation problem\, as it pertains to the prime characteristic sing
 ularity classes of $F$-regular\, $F$-rational\, $F$-pure\, and $F$-injecti
 ve 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 cla
 sses and discuss a recent solution to the deformation of $F$-purity proble
 m in rings which are $\\mathbb{Q}$-Gorenstein. This talk is based on a col
 laboration with Austyn Simpson.\n
LOCATION:https://researchseminars.org/talk/VCAS/73/
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