Chennai Mathematical Institute


3.30 p.m.
Geometry over $\mathbb{F}_1$ and brave new rings

Snigdhayan Mahanta
John Hopkins University, Baltimore.


The base for classical (affine) algebraic geometry is $\mathbb{Z}$. Recently the construction of the strict symmetric monoidal category of spectra enabled us to develop an analogous geometry over the sphere spectrum $\mathbb{S}$ with commutative $\mathbb{S}$-algebras playing the role of affine 'topological' schemes or brave new rings. The geometry over $\mathbb{F}_1$ (somewhat mysteriously called the field with one element) has recently received a lot of attention. I will report on a work in progress relating brave new rings and the geometry over $\mathbb{F}_1$.