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I am a first-year PhD student and I am really interested in Galois module theory, both in a "classical" and in a "nonclassical" sense. In the last months I have been reading about Hopf Galois theory, since it seems to be a nice way to find the structure of the ring of integers (or valuation ring, in the local case), when the classical approach fails.

In particular, I am reading Childs's book "Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory", where he makes a nice exposition of the known facts untile 2000.

I was looking for some more recent results, but my search was not really fruitful. Could you please advise some more modern papers (or books, survey, notes, or anything you want) discussing about Hopf Galois module theory, so Galois module theory applied in the nonclassical setting of Hopf Galois extensions?

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You could try this survey article: MR3415265 Crespo, T. ; Rio, A.; Vela, M. From Galois to Hopf Galois: theory and practice. Trends in number theory, 29–46, Contemp. Math., 649, Amer. Math. Soc., Providence, RI, 2015.

You could also use MathSciNet to look at the list of publications that cite Taming Wild Extensions (there are currently 72 items on that list).

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  • $\begingroup$ Thank you for your answer. Indeed in the survey there is a short final section about Module theory, referring to a pair of other articles. I will also have a look at MathSciNet, but probably most of them cite Childs’s book because it is the standard reference for Hopf Galois theory in general. $\endgroup$
    – Lios
    Commented Mar 16, 2021 at 9:11

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