The large gap in my blog activity over the past months is due largely to my writing time being taken up working on the following extended essay on the basic results in the theory of l-adic cohomology and their applications in proving the Weil conjectures and the theory of Galois representations. It was submitted for Part III of the Mathematical Tripos, the results for which are now known, so publishing it feels appropriate.

Though much of the essay has been drawn from the literature, there are parts which have been restructured or entirely constructed from scratch, and the formality of the presentation should not be mistaken as something that has been peer-reviewed or even very well-checked. However, I hope some people will find it useful and constructive feedback is always appreciated.

Also, if any other (vaguely) current Part III students have published essays online or want to upload theirs, I might consider appending links to this blog post. It would be nice to have a collection of such essays: those which I have read are excellent introductions to more specialist areas pitched at a good level for me and could therefore probably be useful for others.

Etale Cohomology and Galois Representations – Tom Lovering

Friends’ Essays

The Local Langlands Correspondences – Remy van Dobben de Bruyn
Etale Cohomology and Galois Representations (with an emphasis on descent theory) – Low Zhen Lin
p-Adic Uniformisation – Chris Williams
D-modules – Chris Elliott
Multiplicative Coalescence – Dominic Yeo
Tutte’s Flow Conjectures – Laszlo Lovasz