Manchester Algebra Seminar - Shezad Mohammed
|Dates:||18 October 2022|
|Times:||13:00 - 14:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, Current University students|
Speaker: Shezad Mohammed - Manchester
Title. The Weil descent functor in the category of algebras with free operators.
Abstract, 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. This result has since been vastly generalised by Grothendieck and others to the case of arbitrary finite and free extensions of rings and group schemes. In this talk, I will show how we may prove a similar adjunction result about schemes endowed with extra structure, though working algebraically. This extra structure comes from what are known as D-rings, or rings equipped with a finite collection of free operators. A sufficient condition for this adjunction to exist is a mild linear condition on the 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 extensions of D-large fields are again D-large.
Place: Frank Adams (this term the seminar will not be streamed online)
Tea and biscuits 12:45 in the foyer
Travel and Contact Information
Alan Turing Building