Algebra Seminar: Pauwels -- Separable and Galois extensions in symmetric monoidal categories

Bregje Pauwels (Australian National University) 

Friday 1 July, 12-1pm, Place: Carslaw 375 

Separable and Galois extensions in symmetric monoidal categories.

In this talk, I will consider separable (commutative) ring objects in a symmetric 
monoidal category and show how they pop up in various settings. 
In modular representation theory, for instance, restriction to a subgroup can 
be thought of as extension along a separable ring object in the (stable or derived) 
module category. In algebraic geometry, they appear as finite etale extensions of 
affine schemes. But separable ring objects are nice for various reasons, beyond 
the analogy with etale topology; they allow for a notion of degree, have splitting 
ring extensions, and we can define (quasi)-Galois extensions. I will present a 
version of quasi-Galois-descent and give conditions for the existence of a 
quasi-Galois closure.