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SUMMARY:Owen Biesel (Carleton College)
DTSTART:20210503T140000Z
DTEND:20210503T150000Z
DTSTAMP:20260423T022033Z
UID:LAGeNT/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGeNT/9/">A
  norm functor for quadratic algebras</a>\nby Owen Biesel (Carleton College
 ) as part of Leiden Algebra\, Geometry\, and Number Theory Seminar\n\n\nAb
 stract\nThe trace and norm maps from Galois theory are two members of a me
 nagerie of various norm functors for different types of algebraic data: gi
 ven a ring R with a finite locally-free algebra A (both commutative and un
 ital)\, we can take the trace or norm of an element of A to get an element
  of R\, we can take the "norm" of a line bundle over A to get a line bundl
 e over R\, and thanks to Ferrand we can even take an arbitrary A-module an
 d construct its "norm" as an R-module. In this talk we construct a norm fu
 nctor for the data of a quadratic algebra: given a locally-free rank-2 A-a
 lgebra D\, we produce a locally-free rank-2 R-algebra Nm(D) in a way that 
 is compatible with other norm functors and which extends a known construct
 ion for étale quadratic algebras. We also conjecture a relationship betwe
 en discriminant algebras and this new norm functor.\n
LOCATION:https://researchseminars.org/talk/LAGeNT/9/
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