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SUMMARY:Vaidehee Thatte
DTSTART:20211124T100000Z
DTEND:20211124T110000Z
DTSTAMP:20260423T022143Z
UID:viasmag/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/viasmag/3/">
 Arbitrary Valuation Rings and Wild Ramification</a>\nby Vaidehee Thatte as
  part of VIASM Arithmetic Geometry Online Seminar\n\nLecture held in C101\
 , VIASM.\n\nAbstract\nClassical ramification theory deals with complete di
 screte valuation fields $k((X))$ with perfect residue fields $k$. Invarian
 ts such as the Swan conductor capture important information about extensio
 ns of these fields. Many fascinating complications arise when we allow non
 -discrete valuations and imperfect residue fields $k$. Particularly in pos
 itive residue characteristic\, we encounter the mysterious phenomenon of t
 he defect (or ramification deficiency). The occurrence of a non-trivial de
 fect is one of the main obstacles to long-standing problems\, such as obta
 ining resolution of singularities in positive characteristic.\n\n\nDegree 
 $p$ extensions of valuation fields are building blocks of the general case
 . In this talk\, we will present a generalization of ramification invarian
 ts for such extensions and discuss how this leads to a better understandin
 g of the defect. If time permits\, we will briefly discuss their connectio
 n with some recent work (joint with K. Kato) on upper ramification groups.
 \n
LOCATION:https://researchseminars.org/talk/viasmag/3/
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