@inbook{86976ec6ee5345df932eafa63388f7ed,

title = "Metrization of Differential Pluriforms on Berkovich Analytic Spaces",

abstract = "We introduce a general notion of a seminorm on sheaves of rings or modules and provide each sheaf of relative differential pluriforms on a Berkovich k-analytic space with a natural seminorm, called K{\"a}hler seminorm. If the residue field k~ is of characteristic zero and X is a quasi-smooth k-analytic space, then we show that the maximality locus of any global pluricanonical form is a PL subspace of X contained in the skeleton of any semistable formal model of X. This extends a result of Musta{\c t}{\u a} and Nicaise, because the K{\"a}hler seminorm on pluricanonical forms coincides with the weight norm defined by Musta{\c t}{\u a} and Nicaise when k is discretely valued and of residue characteristic zero.",

keywords = "Berkovich analytic spaces, K{\"a}hler seminorms, Pluriforms",

author = "Michael Temkin",

year = "2016",

doi = "10.1007/978-3-319-30945-3_8",

language = "אנגלית",

isbn = "9783319309446",

series = "Simons Symposia",

publisher = "Springer International Publishing AG",

pages = "195–285",

booktitle = "Nonarchimedean and Tropical Geometry",

address = "שוויץ",

}