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SUMMARY:Understanding the Defect via Ramification Theory - Vaidehee Thatte
 \, King's College London
DTSTART:20220215T143000Z
DTEND:20220215T153000Z
UID:TALK169478@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:Classical ramification theory deals with complete discrete val
 uation fields k((X)) with perfect residue fields k. Invariants such as the
  Swan conductor capture important information about extensions of these fi
 elds. Many fascinating complications arise when we allow non-discrete valu
 ations and imperfect residue fields k. Particularly in positive residue ch
 aracteristic\, we encounter the mysterious phenomenon of the defect (or ra
 mification deficiency). The occurrence of a non-trivial defect is one of t
 he main obstacles to long-standing problems\, such as obtaining resolution
  of singularities in positive characteristic.\nDegree p extensions of valu
 ation fields are building blocks of the general case. In this talk\, I wil
 l present a generalization of ramification invariants for such extensions 
 and discuss how this leads to a better understanding of the defect. If tim
 e permits\, I will briefly discuss their connection with some recent work 
 (joint with K. Kato) on upper ramification groups.\n
LOCATION:https://maths-cam-ac-uk.zoom.us/j/92192959944?pwd=OVJ3d0pJS3RRaWh
 KOVBuMFJIM3FiQT09
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