Jesse Kass
Pathologies in Characteristic p: The Picard Scheme

The Picard scheme of a smooth projective variety X is a scheme that parameterizes line bundles on X.  When X is a curve, the identity component of the Picard scheme is the Jacobian.  When X is defined over a characteristic 0 field, the Picard scheme is always an abelian variety. Surprisingly, the Picard scheme can be non-reduced when X is defined over a field of positive characteristic.

In my talk, I will discuss some example of this phenomenon due to Igusa and Serre and some related results due to Mumford.