A norm functor for quadratic algebras

Owen Biesel (Carleton College)

03-May-2021, 14:00-15:00 (3 years ago)

Abstract: The trace and norm maps from Galois theory are two members of a menagerie of various norm functors for different types of algebraic data: given a ring R with a finite locally-free algebra A (both commutative and unital), 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 bundle over R, and thanks to Ferrand we can even take an arbitrary A-module and construct its "norm" as an R-module. In this talk we construct a norm functor for the data of a quadratic algebra: given a locally-free rank-2 A-algebra 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 construction for étale quadratic algebras. We also conjecture a relationship between discriminant algebras and this new norm functor.

algebraic geometrynumber theory

Audience: researchers in the topic


Leiden Algebra, Geometry, and Number Theory Seminar

Organizers: Marton Hablicsek*, Aline Zanardini*
*contact for this listing

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