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SUMMARY:Thomas Polstra (University of Virgina)
DTSTART:20210312T130000Z
DTEND:20210312T140000Z
DTSTAMP:20260423T021002Z
UID:VCAS/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/72/">St
 rongly F-regular rings\, maximal Cohen-Macaulay modules\, and the F-signat
 ure</a>\nby Thomas Polstra (University of Virgina) as part of IIT Bombay V
 irtual Commutative Algebra Seminar\n\n\nAbstract\nThe singularities of a l
 ocal prime characteristic ring are best understood through the behavior of
  the Frobenius endomorphism. A singularity class of central focus is the c
 lass of strongly $F$-regular rings. Examples of strongly $F$-regular rings
  include normal affine toric rings\, direct summands of regular rings\, an
 d determinantal rings. Every strongly $F$-regular ring enjoys the property
  of being a normal Cohen-Macaulay domain. In particular\, the study of fin
 itely generated maximal Cohen-Macaulay modules over such rings is a warran
 ted venture. We will demonstrate a surprising uniform behavior enjoyed by 
 the category of maximal Cohen-Macaulay modules over a strongly $F$-regular
  local ring. Consequently\, we can redrive Aberbach and Leuschke's theorem
  that the $F$-signature of a strongly $F$-regular ring is positive in a no
 vel and elementary manner. Time permitting\, we will present applications 
 on the structure of the divisor class group of a local strongly $F$-regula
 r ring.\n
LOCATION:https://researchseminars.org/talk/VCAS/72/
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