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Representations of higher adelic groups and arithmetic. (English) Zbl 1266.11118

Bhatia, Rajendra (ed.) et al., Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19–27, 2010. Vol. I: Plenary lectures and ceremonies. Hackensack, NJ: World Scientific; New Delhi: Hindustan Book Agency (ISBN 978-981-4324-30-4/set; 978-81-85931-08-3/hbk; 978-981-4324-31-1/hbk; 978-981-4324-35-9/ebook). 362-392 (2011).
The paper under review discusses various problems and results concerning higher dimensional local fields and adelic groups. The main topics include:
1) measure theory and harmonic analysis on higher local fields and adelic groups,
2) extending of Tate-Iwasawa’s analytic method to higher dimensions,
3) behaviour of zeta- and \(L\)-functions,
4) representations of discrete and adelic Heisenberg groups.
The paper also includes a rich bibliography on these subjects.
For the entire collection see [Zbl 1220.00031].

MSC:

11R56 Adèle rings and groups
11S31 Class field theory; \(p\)-adic formal groups
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