ModSles semi-factoriels et modSles de N,ron

作者：Pepin Cedric^*

来源：Mathematische Annalen, 2013, 355(1): 147-185.

DOI：10.1007/s00208-012-0784-2

Let S be the spectrum of a discrete valuation ring with function field K. Let X be a scheme over S. We will say that X is semi-factorial over S if any invertible sheaf on the generic fiber X (K) can be extended to an invertible sheaf on X. Here we show that any proper geometrically normal scheme over K admits a proper, flat, normal and semi-factorial model over S. We also construct some semi-factorial compactifications of regular S-schemes, such as N,ron models of abelian varieties. The semi-factoriality property for a scheme X/S corresponds to the N,ron property of its Picard functor. In particular, one can recover the N,ron model of the Picard variety of X (K) from the Picard functor Pic (X/S) , as in the known case of curves. This provides some information on the relative algebraic equivalence on the S-scheme X.

• 出版日期2013-1