An overview of the ladic and padic monodromy theorems
An overview of the ladic and padic monodromy theorems

Stefan Patrikis, Princeton University
Fine Hall 314
I will introduce (focusing on the case of elliptic curves) two essential theorems of arithmetic geometry that bind the geometry of an algebraic variety over a local field (or number field) to its arithmetic, Galoistheoretic properties. The ladic monodromy theorem is in fact entirely elementary (one needn't even know what 'monodromy' means!) but will motivate the subtler padic theorem. Together these results will help us make sense of the FontaineMazur conjecture, one of the fundamental open problems in arithmetic geometry.