Algebra Seminar: Lanfranchi -- Representable tangent structures for affine schemes

Marcello Lanfranchi (Macquarie University) will be speaking in the algebra seminar.  We
will go out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday August 22 

Where: Carslaw 175 

Title: Representable tangent structures for affine schemes 

Abstract: Tangent category theory is a categorical framework for differential geometry.
In recent work, tangent categories were also employed to study algebraic geometry.  In
particular, the category of affine schemes is a tangent category whose tangent bundle is
given by Kahler differentials.  How special is this tangent structure? Is there any
other tangent structure on the category of affine schemes? In this talk, we classify the
representable tangent structures in the category of affine schemes by introducing the
new notion of tangentoids.  When the base ring R is a principal ideal domain, we show
there are only two such tangent structures: the aforementioned one, and the trivial
one.  We also show that when R is not a PID, we have other non-trivial representable
tangent structures.  

This is joint work with JS Lemay.  

Paper: https://arxiv.org/abs/2505.09080