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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
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  • Department of Mathematics

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  • In category "Seminar"
  • In group "(Maths) Algebra"
  • In group "(Maths) Maths seminar series"
  • By Department of Mathematics

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

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Frank Adams
Alan Turing Building
Manchester

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Kieran Calvert

kieran.calvert@manchester.ac.uk

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