On the semicontinuity problem of fibers and global F-regularity

Details On the semicontinuity problem of fibers and global F-regularity On the semicontinuity problem of fibers and global F-regularity

2011-11-13

arxiv.org/abs/1111.3020v1

Mathematics

Algebraic Geometry

23 pages

Scientific paper

In this article, we discuss the semicontinuity problem of certain properties on fibers for a morphism of Noetherian schemes. One aspect of this problem is local. Namely, we consider properties of schemes at the level of local rings, in which the main results are established by solving the lifting and localization problems for local rings. In particular, we obtain the localization theorem in the case of seminormal and F-rational rings, respectively. The second aspect is the global issue, which is related to the vanishing problem of certain higher direct image sheaves. We discuss the deformation of globally F-regular varieties in this case.

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