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CATEGORIES:Number Theory Seminar
SUMMARY:Understanding the Defect via Ramification Theory -
Vaidehee Thatte\, King's College London
DTSTART;TZID=Europe/London:20220215T143000
DTEND;TZID=Europe/London:20220215T153000
UID:TALK169478AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/169478
DESCRIPTION:Classical ramification theory deals with complete
discrete valuation fields k((X)) with perfect resi
due fields k. Invariants such as the Swan conducto
r capture important information about extensions o
f these fields. Many fascinating complications ari
se when we allow non-discrete valuations and imper
fect residue fields k. Particularly in positive re
sidue characteristic\, we encounter the mysterious
phenomenon of the defect (or ramification deficie
ncy). The occurrence of a non-trivial defect is on
e of the main obstacles to long-standing problems\
, such as obtaining resolution of singularities in
positive characteristic.\nDegree p extensions of
valuation fields are building blocks of the genera
l case. In this talk\, I will present a generaliza
tion of ramification invariants for such extension
s and discuss how this leads to a better understan
ding of the defect. If time permits\, I will brief
ly 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=
OVJ3d0pJS3RRaWhKOVBuMFJIM3FiQT09
CONTACT:Rong Zhou
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