Derived direct summands -- Bhargav Bhatt, April 16, 2010

A variety satisfies the direct summand condition if its structure sheaf is a summand of that of a finite cover; in characteristic 0, this condition reduces to normality. We will discuss a derived category enrichment of this condition. The two conditions diverge in characteristic 0 (the latter characterises rational singularities), but turn out to be very closely related in positive and mixed characteristic. Using this relation, I will also discuss some applications, including extensions of standard cohomological vanishing results beyond the ample cone in positive characteristic algebraic geometry.