Algebra Seminar: Transcendental Field Extensions and Unbounded Representation Type

Abstract: The classical first Brauer-Thrall conjecture, first proved by Roiter, states that if a finite-dimensional algebra has infinitely many non-isomorphic finite-dimensional modules, then the dimensions of these modules are unbounded. Among other results, we extend this statement to constructible subcategories of the module category of a finitely generated algebra. Such subcategories are defined by a single finiteness condition imposed by a finitely presented functor. The proof relies on a combination of techniques from representation theory, algebraic geometry, and model theory. In particular, we study purely transcendental field extensions of transcendence degree one and exploit the interaction between geometric methods and the model theory of modules, with the Ziegler spectrum playing an important role.

Attend in person or via Zoom: https://uu-se.zoom.us/j/64555726999, (please contact the organiser for passcode)

This is a seminar in our algebra seminar series.