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.

Add to your calendar

Download event information as iCalendar file (only this event)