# Geir Ellingsrud (UiO): On a reconstruction theorem of Kollár, Lieblich, Olsson and Sawin

When does the Zariski topology determine a variety? This certainly does not hold for curves, and examples of Wiegand and Krauter show it is neither true for countable surfaces. The cardinality assumption is important: The reconstruction theorem says that two homeomorphic (normal, projective) varieties of dimension at least two over non-countable fields of characteristic zero K and L (a priori different) are in fact isomorphic (as schemes).

I shall present my version (a slight simplification of the original proof) of the cluster of ideas leading up to the reconstruction theorem (and maybe a miniscule extension to positive characteristic)

Published Nov. 5, 2021 12:02 PM
- Last modified Nov. 16, 2021 8:00 AM