Dolbeault cohomology of weakly smooth forms on non-archimedean abelian varieties

URN to cite this document:: urn:nbn:de:bvb:355-epub-544656
DOI to cite this document:: 10.5283/epub.54465

Prechtel, Miriam

License: Creative Commons Attribution 4.0
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Date of publication of this fulltext: 12 Jul 2023 10:33

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Item type:	Thesis of the University of Regensburg (PhD)
Open Access Type:	Primary Publication
Date:	12 July 2023
Referee:	Prof. Dr. Klaus Künnemann
Date of exam:	6 July 2023
Institutions:	Mathematics Mathematics > Prof. Dr. Klaus Künnemann
Keywords:	Berkovich analytic spaces, non-archimedean geometry, abelian varieties, Dolbeault cohomology, weakly smooth forms, first Chern form, tropical geometry, Raynaud extension, Delta-forms
Dewey Decimal Classification:	500 Science > 510 Mathematics
Status:	Published
Refereed:	Yes, this version has been refereed
Created at the University of Regensburg:	Yes
Item ID:	54465

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Abstract (English)

We investigate the Dolbeault cohomology of weakly smooth forms on the Berkovich analytification of abelian varietes over a complete, non-trivially valued, non-archimedean field. In this setting, we give lower bounds for the dimension of the Dolbeault cohomology groups of weakly smooth forms. Furthermore, we prove lower bounds for the dimension of the Dolbeault cohomology groups of strong currents, i.e. of the topological dual of weakly smooth forms, in higher degrees.

Translation of the abstract (German)

Wir untersuchen die Dolbeault Kohomologie von schwach-glatten Formen auf der Berkovich Analytifizierung von abelschen Varietäten über vollständigen, nicht-trivial bewerteten nicht-archimedischen Körpern. In diesem Setup geben wir einerseits untere Schranken für die Dimension der Dolbeault Kohomologie Gruppen der schwach-glatten Formen an. Andererseits erhalten wir auch untere Schranken für die ...