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VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20221010T140133Z
DTSTART:20221018T120000Z
DTEND:20221018T130000Z
SUMMARY:Manchester Algebra Seminar - Shezad Mohammed
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}q8z-l81h2hk
8-vo52t0
DESCRIPTION:Speaker: Shezad Mohammed - Manchester\n\nTitle. The Weil des
cent functor in the category of algebras with free operators.\n\nAbstrac
t\, Weil restriction is a result of algebraic geometry that says that if
L/K is a finite extension of fields\, then base change\, considered as
a functor from schemes over K to schemes over L\, has a right adjoint. T
his result has since been vastly generalised by Grothendieck and others
to the case of arbitrary finite and free extensions of rings and group s
chemes. In this talk\, I will show how we may prove a similar adjunction
result about schemes endowed with extra structure\, though working alge
braically. This extra structure comes from what are known as D-rings\, o
r rings equipped with a finite collection of free operators. A sufficien
t condition for this adjunction to exist is a mild linear condition on t
he associated endomorphisms of the base D-rings\, and we will show that\
, in the case of fields\, this is also a necessary condition. Finally\,
we will see how this result may be used to show that algebraic extension
s of D-large fields are again D-large.\n\n\nPlace: Frank Adams (this ter
m the seminar will not be streamed online)\n\n\nTea and biscuits 12:45 i
n the foyer
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams\, Alan Turing Building\, Manchester
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