Daniel Windisch: On divisors of locally complete intersection schemes
Daniel Windisch (Graz University of Technology, Austria)
On divisors of locally complete intersection schemes
Abstract: Samuel conjectured in 1961 that a (Noetherian) local complete intersection ring which is a UFD (unique factorization domain) in codimension at most three is itself a UFD. It is said that Grothendieck invented local cohomology to prove this fact. Having in mind that a UFD is nothing else than a normal domain with trivial divisor class group, I will present a generalization of the Samuel--Grothendieck Theorem without restrictions on the divisor class groups in codimension three and less. This result can be used to prove that, for an integral Noetherian scheme that is locally a complete intersection, the gap between Weil and Cartier divisors does only depend on information in codimension at most three.
Roman Drnovšek in Primož Moravec