# Thesis

### PhD Thesis:

Neron-Tate heights on the Jacobians of high-genus hyperelliptic curves

My viva (oral examination for PhD) was on 29 August 2012. I passed with minor corrections, which were accepted by the examiners on 14 September 2012. I plan to graduate in January 2013.

The first 4 chapters are essentially known material presented as background. Chapter 5 is my arxiv paper here. Chapter 6 gives a new definition of a naive height and proves that it has bounded difference from the Neron-Tate height. Chapter 7 uses this to give an algorithm for saturation on a hyperelliptic Jacobian - that is, the process of finding a basis of the Mordell-Weil group once a finite-index subgroup has been found by descent.

### "Master's thesis":

Fibrations

I attended Part III in Cambridge, during which I wrote the above essay under the supervision of Caucher Birkar. Since Part III has since been upgraded to a master's course, maybe this is now considered a master's thesis...

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