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Bertini theorems for hypersurface sections containing a subscheme over finite fields

Wutz, Franziska (2015) Bertini theorems for hypersurface sections containing a subscheme over finite fields. PhD, Universität Regensburg.

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Date of publication of this fulltext: 07 May 2015 16:49

Abstract (English)

In this thesis we show the existence of a hypersurface that contains a given closed subscheme of a projective space over a finite field and intersects a smooth quasi-projective scheme smoothly, under some condition on the dimension. This generalizes a Bertini theorem by Bjorn Poonen; the proof uses a closed point sieve introduced by him. Furthermore, we add the possibility of modifying finitely many local conditions of the hypersurface.

Translation of the abstract (German)

In dieser Arbeit zeigen wir die Existenz einer Hyperfläche, die ein gegebenes abgeschlossenes Unterschema des projektiven Raums über einem endlichen Körper enthält und ein glattes quasi-projektives Schema glatt schneidet, unter einer Bedingung an die Dimension. Dies verallgemeinert einen Bertini-Satz von Bjorn Poonen; der Beweis verwendet einen Siebbeweis, den er eingeführt hat. Außerdem zeigen wir, dass wir in endlich vielen Punkten lokale Bedingungen an die Hyperfläche stellen können.


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Item type:Thesis of the University of Regensburg (PhD)
Date:7 May 2015
Referee:Prof. Dr. Uwe Jannsen
Date of exam:28 January 2015
Institutions:Mathematics > Prof. Dr. Uwe Jannsen
Keywords:Bertini theorem over finite fields, smooth hypersurface section, closed point sieve
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:31668
Owner only: item control page

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