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I'm just about to start my final year of undergrad. I need to choose a thesis title but I'm having some trouble. I know a little Galois Cohomology and would really like to learn more. The prof who is supervising me said he is not keen on me doing a project on Galois cohomology because it is 'just a tool'.

Is this true?


Any suggestions for a thesis title which will allow me to learn Galois cohomology while not being totally direction-less; a project which has a 'direction'?


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closed as not constructive by Rasmus, M Turgeon, Did, Sasha, Qiaochu Yuan Sep 17 '12 at 18:39

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Did you ask the professor supervising you what he meant by "it is just a tool"? That's probably how you will get the best answer to your question. –  M Turgeon Sep 17 '12 at 17:26
Nonetheless, an area of mathematics where Galois cohomology is amply used is (algebraic) number theory. In general, cohomology measures "obstructions"; in Galois cohomology, you measure the obstruction to having a rational structure. As for a reference about general Galois cohomology (with some applications), have a look at both Serre's Galois cohomology and Berhuy's An introduction to Galois cohomology. –  M Turgeon Sep 17 '12 at 17:29
Maybe you could learn Galois cohomology with the goal of understanding Poitou-Tate global duality. –  Keenan Kidwell Sep 17 '12 at 17:33
It is usually best to pick the title after you've already a significant part of your thesis, nor the other way round! –  Mariano Suárez-Alvarez Sep 17 '12 at 18:07
As a sample, here is a senior thesis on Galois cohomology (written by one of my colleagues). –  user31373 Sep 17 '12 at 19:57