Purity and pp formulas for sheaves
Samuel Dean (University of Glasgow)
Wednesday 7th March, 2018 16:00-17:00 Maths 311B
Estrada, Enochs and Odabasi gave a defition of what it should mean for a sheaf to sit inside another sheaf as a pure substructure. This is done in a locally algebraic fashion. But in the model theory of modules, we know well that this condition can be said in terms of pp formulas. Sheaves, not usually being 1st-order structures, can't obviously be approached like this. When we are concerned with a nice class of sheaves which are secretly 1st-order structures, a categorical approach to purity can be taken. However, these categorical notions are intrinsically global, and often have disappointingly trivial properties, because they do not respect the local nature of sheaves. I will give a notion of a pp formula for sheaves which fits with the local notion of purity, and explain what the remaining questions are.