Weber, Andreas (2015) Intersection theory on regular schemes via alterations and deformation to the normal cone. PhD, Universität Regensburg.
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Abstract (English)
In order to generalize Arakelov's arithmetic intersection theory from arithmetic surfaces to higher dimensions, Gillet and Soulé introduced an intersection product with supports for any Noetherian separated regular scheme, after tensoring the Chow groups with support by Q. We develope an alternative approach for such an intersection product, which uses Fulton's method of deformation to the normal cone and de Jong's result on alterations.
Translation of the abstract (German)
Um Arakelov's arithmetische Schnitttheorie von arithmetischen Flächen auf höhere Dimensionen zu verallgemeinern, führten Gillet und Soulé ein Schnittprodukt mit Träger für jedes Noethersche separierte reguläre Schema ein, nachdem die Chowgruppen mit Q tensoriert werden. In der Arbeit wird ein alternativer Zugang für ein solches Schnittprodukt entwickelt, welches Fultons Deformation in das Normalenbündel und de Jongs Resultat über Alterationen benützt.
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| Item type: | Thesis of the University of Regensburg (PhD) |
|---|---|
| Date: | 29 May 2015 |
| Referee: | Prof. Dr. Klaus Künnemann |
| Date of exam: | 21 May 2015 |
| Institutions: | Mathematics > Prof. Dr. Klaus Künnemann |
| Keywords: | intersection theory, arithmetic geometry, intersection theory with supports, intersection theory on regular schemes, Arakelov, arithmetic intersection theory |
| 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: | 31887 |
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