F-singularities and weak ordinarity

Series: 
Algebra Seminar
Monday, October 20, 2014 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
University of Utah
Organizer: 
I will discuss recent work of Bhargav Bhatt, myself and Shunsuke Takagi relating several open problems and generalizing work of Mustata and Srinivas. First: whether a smooth complex variety is ordinary after reduction to characteristic $p > 0$ for infinitely many $p$. Second: that multiplier ideals reduce to test ideals for infinitely many $p$ (regardless of coefficients). Finally, whether complex varieties with Du Bois singularities have $F$-injective singularities after reduction to infinitely many $p > 0$.