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SUMMARY:Approximation of perfectoid rings by Noetherian rings and prisms [
 MPIM]
DTSTART:20250527T120000Z
DTEND:20250527T133000Z
DTSTAMP:20260415T092200Z
UID:indico-event-266@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ryo Ishizuka (Institute of Science Tokyo)\n\nAlgebra
  seminar\nThe theory of perfectoid towers\, introduced by Ishiro-Nakazato-
 Shimomoto\, provides an axiomatic approach to perfectoid theory in commuta
 tive algebra through tower-theoretic approximations. In contrast\, Bhatt a
 nd Scholze introduced prisms as a "deperfection" of perfectoid rings. Our 
 main result shows that a "gradual perfection" of a prism becomes a perfect
 oid tower. As a consequence\, we prove that any p-torsion-free p-adically 
 complete delta-ring that is reduced modulo p admits a perfectoid tower. Th
 is approach allows for more systematic construction of perfectoid rings an
 d towers from Noetherian rings than previously possible. We also provide n
 ew examples of perfectoid towers arising from certain singularities\, whic
 h were inaccessible by previous methods. In this talk\, we will review the
  concepts of perfectoid towers\, explain our construction from prisms\, an
 d demonstrate its applications through these novel examples.\n\nhttps://ma
 th-events.uni-bonn.de/event/266/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/266/
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