Metrization of Differential Pluriforms on Berkovich Analytic Spaces

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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 Kähler 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 Mustaţă and Nicaise, because the Kähler seminorm on pluricanonical forms coincides with the weight norm defined by Mustaţă and Nicaise when k is discretely valued and of residue characteristic zero.
Original languageEnglish
Title of host publicationNonarchimedean and Tropical Geometry
PublisherSpringer International Publishing AG
Number of pages91
ISBN (Print)9783319309446, 9783319309453
StatePublished - 2016

Publication series

NameSimons Symposia
ISSN (Print)2365-9564
ISSN (Electronic)2365-9572


  • Berkovich analytic spaces
  • Kähler seminorms
  • Pluriforms


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