Here you can see my PhD thesis, *Computations on Diagonal
Quartic Surfaces*, for which I studied at the University of Cambridge
under Sir Peter Swinnerton-Dyer. My thesis was examined on 11th
November 2002 by Prof. Victor Flynn (Liverpool) and Dr Tom Fisher
(Cambridge).

- Read the summary in DVI, PostScript or PDF format.
- Read the whole thesis in DVI, PostScript or PDF format.

**Erratum:** Lemma 4.5 is incorrect. The proof given
relies on Lang's theorem, the reference cited being Milne's lecture
notes: in fact, the statement there is missing the hypothesis that
the ring should be one-dimensional, and Lang's theorem does not apply
here. The following corollary, 4.6, and
subsequent statements, are nonetheless true;
but the proof relies on the purity theorem for the Brauer group.

Various bits of data and implementations of algorithms described in my thesis may be downloaded from my diagonal quartic surfaces page.

Martin Bright

Last modified: 26 March 2008