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SUMMARY:Vaidehee Thatte (King's College London)
DTSTART:20211208T150000Z
DTEND:20211208T160000Z
DTSTAMP:20260418T063835Z
UID:LNTS/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/48/">Un
 derstanding the Defect via Ramification Theory</a>\nby Vaidehee Thatte (Ki
 ng's College London) as part of London number theory seminar\n\nLecture he
 ld in Huxley 144\, Imperial.\n\nAbstract\nClassical ramification theory de
 als with complete discrete valuation fields $k((X))$ with perfect residue 
 fields $k$. Invariants such as the Swan conductor capture important inform
 ation about extensions of these fields. Many fascinating complications ari
 se when we allow non-discrete valuations and imperfect residue fields $k$.
  Particularly in positive residue characteristic\, we encounter the myster
 ious phenomenon of the defect (or ramification deficiency). The occurrence
  of a non-trivial defect is one of the main obstacles to long-standing pro
 blems\, such as obtaining resolution of singularities in positive characte
 ristic.\n\nDegree p extensions of valuation fields are building blocks of 
 the general case. In this talk\, we will present a generalization of ramif
 ication invariants for such extensions and discuss how this leads to a bet
 ter understanding of the defect. If time permits\, we will briefly discuss
  their connection with some recent work (joint with K. Kato) on upper rami
 fication groups.\n
LOCATION:https://researchseminars.org/talk/LNTS/48/
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