In this thesis we introduce the notion of a cdp-functor on the category of proper schemes over a Noetherian base, and we show that cdp-functors to Waldhausen categories extend to factors that satisfy the excision property. This allows us to associate with a cdp-functor an Euler-Poincaré characteristic that sends the class of a proper scheme to the class of its image. Applying this construction to the Yoneda embedding yields a monoidal proper-fibred Waldhausen category over Noetherian schemes, with canonical cdp-functors to its fibres. Also, we deduce a motivic measure to the Grothendieck ring of finitely presented simplicially stable motivic spaces with the cdh-topology.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:722106 |
| Date | January 2017 |
| Creators | Alameddin, A. |
| Publisher | University of Liverpool |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://livrepository.liverpool.ac.uk/3007868/ |
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