Student Arithmetic Geometry Seminar: Bertini Theorems over Finite Fields

Seminar | October 25 | 4:10-5 p.m. | 891 Evans Hall

 Anya Michaelsen, UC Berkeley

 Department of Mathematics

The Bertini Theorems prove smoothness of the intersection of smooth varieties with generic hyperplanes when working in projective space over infinite fields. However, over a finite field, even the existence of such a hyperplane can fail. Using hypersurfaces instead of hyperplanes, we will state a modified Bertini Theorem for finite fields due to Poonen. We then give a brief intuition for the result and consider a specific example involving square-free polynomials.