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PRODID:-//Memento EPFL//
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SUMMARY:Dual F-signature
DTSTART:20240521T141500
DTEND:20240521T160000
DTSTAMP:20260601T231028Z
UID:8e1937c8fb56d660f54c4c285484db1beb305be95db786eac2b5203b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ilya Smirnov (BCAM)\nI will report on the joint work with Kevi
 n Tucker which completed the basics of the theory of dual F-signature/F-ra
 tional signature. \n\nF-signature is a volume-like invariant of singulari
 ties of positive characteristic: its minimal value\, 0\, characterises the
  class of strongly F-regular singularities and its maximal value\, 1\, det
 ects non-singularity. Hence\, F-signature stratifies the class of strongly
  F-regular singularities. F-signature is now reasonably well-understood an
 d has strong applications in algebraic geometry\, for example\, giving an 
 explicit bound on the size of the local étale fundamental group.\n\nThe c
 lass of F-rational singularities is more severe than the class of F-regula
 r singularities\, but is closely related. For example\, after work of Smit
 h\, Vélez\, and Blickle one can think about F-rationality as F-regularity
  of the dualising module. Due to the close connection\, it was expected th
 at there should an F-signature like invariant for F-rationality and two di
 stinct definitions were given: dual F-signature by Sannai and F-rational s
 ignature of Hochster — Yao. \n\nThe main result of our work is that\, a
 fter a normalization\, the Hochster—Yao signature is equal to Sannai’s
 . This allows combination of the techniques that results in a theory almos
 t parallel to that of F-signature.
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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