As is by now well known, Tu proved in 1998 that the C*-algebras coming from amenable groupoids satisfy the so-called UCT (universal coefficient theorem). Unfortunately, I don't speak french and I've only found this result in french.

Question: does anyone happen to know of any account of the proof that is written in English?

Tu's original paper is fairly long, and hence would require a lot of work to read for a non-speaker. Even talks available online, or particular cases (such as the same for amenable groups) would be helpful and very much appreciated.

[1] J.L. Tu, La conjecture de Baum–Connes pour les feuilletages moyennables, K-Theory 17 (1999) pp. 215–264, (pdf)


1 Answer 1


For anyone that might see this in the future, in the chapter 12 of here you may find a short summary of the main ideas of Tu's proof.


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