# 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.

Vljudno vabljeni.

Roman Drnovšek in Primož Moravec