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SUMMARY:Cristhian Garay (Centro de Investigación en Matemáticas (CIMAT)\
 , Guanajuato)
DTSTART:20230206T190000Z
DTEND:20230206T200000Z
DTSTAMP:20260423T021137Z
UID:NTC/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/12/">Gen
 eralized valuations and idempotization of schemes</a>\nby Cristhian Garay 
 (Centro de Investigación en Matemáticas (CIMAT)\, Guanajuato) as part of
  Lethbridge number theory and combinatorics seminar\n\nLecture held in Uni
 versity of Lethbridge: M1040 (Markin Hall).\n\nAbstract\nClassical valuati
 on theory has proved to be a valuable tool in number theory\, algebraic ge
 ometry and singularity theory. For example\, one can enrich spectra of rin
 gs with new points coming from valuations defined on them and taking value
 s in totally ordered abelian groups.\n\n\n\nTotally ordered groups are exa
 mples of idempotent semirings\, and generalized valuations appear when we 
 replace totally ordered abelian groups with more general idempotent semiri
 ngs. An important example of idempotent semiring is the tropical semifield
 . \n\n\nAs an application of this set of ideas\, we show how to associate 
 an idempotent version of the structure sheaf of a scheme\, which behaves p
 articularly well with respect to idempotization of closed subschemes.\n\n\
 nThis is a joint work with Félix Baril Boudreau.\n
LOCATION:https://researchseminars.org/talk/NTC/12/
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