Can I find some interesting applications of homological algebra in algebraic number theory? I need some references. Thank you in advanced!
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You may be interested in Galois cohomology, which in my opinion is a very beautiful subject. As always, a good place to start is https://en.wikipedia.org/wiki/Galois_cohomology. Another good reference is a book of Serre's called Cohomologie Galoisienne which has an english translation published by Springer.
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$\begingroup$ It is advanced for a first year master student? $\endgroup$– rafaCommented Nov 11, 2016 at 13:15
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$\begingroup$ @rafa for a graduate student without the necessary background the Serre book may be prohibitive. There are these notes of William Stein of Washington University (link: wstein.org/edu/2010/582e/lectures/all/galois_cohomology.pdf) which may be more appropriate. $\endgroup$ Commented Nov 11, 2016 at 13:20