Abstract:  

I will report on joint work in progress with Akshay Venkatesh. Motivated by anomalous class group statistics, we propose an arithmetic analogue of the topological story of quadratic enhancements associated with spin structures on closed oriented $2$- and $3$-manifolds: a choice of spin structure gives, respectively, a quadratic refinement of the mod $2$ intersection form and of the linking pairing on the first torsion homology. Time permitting, I will clarify the sense in which our construction can be viewed as a candidate determinant-of-cohomology for number fields.

Organizer: Heng Du (Tsinghua University)