This lecture series is based on the 6 lectures I gave at the instructional workshop "Iwasawa Theory over function fields" at ICMAT (Madrid, Spain). The aim of this lecture series is to explain the formulation of the equivariant BSD conjecture over global function fields, following the joint work with D. Burns and M. Kakde. We now explain the statement of the equivariant BSD conjecture.

In four-dimensional topology, the smooth and topological categories have significant differences, called exotica. For instance, there are many smooth manifolds that are homeomorphic but not diffeomorphic. Moreover, there are many smoothly embedded surfaces in a 4-manifold that are isotopic topologically, but not smoothly. In this talk, we explore how exotic phenomena can be constructed and detected via knots.

This lecture series is based on the 6 lectures I gave at the instructional workshop "Iwasawa Theory over function fields" at ICMAT (Madrid, Spain). The aim of this lecture series is to explain the formulation of the equivariant BSD conjecture over global function fields, following the joint work with D. Burns and M. Kakde. In the next two--three talks, I will explain the backgrounds on K_1 and relative K_0 of group rings for finite groups over local/global fields of characteristic 0 and their orders.