Ivan Borisovich Fessenko

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Iwan Borissowitsch Fessenko ( Russian Иван Борисович Фесенко , English transcription Ivan Fesenko ; * 1962 ) is a Russian mathematician who deals with number theory and arithmetic geometry.

Life

Fesenko studied at the Leningrad State University , where he received his doctorate in 1987 under Sergei Vladimirovich Vostokow ( Explicit Constructions in Local Class Field Theory ). He is a professor at the University of Nottingham .

It deals with generalizations of class field theory and other concepts of number theory in higher dimensions, for example with the help of so-called higher dimensional local fields , a concept introduced by Parschin and Kazuya Kato in the 1970s (the zero-dimensional case is finite fields, for example) . The aim is to study the arithmetic of higher-dimensional objects (arithmetic schemes ). To this end, he developed tools that transfer concepts from measurement theory , topology and analysis (such as Fourier transformation ) to higher-dimensional situations in a corresponding manner. Kazuya Kato (early 1980s) and Fesenko developed a local higher class field theory in which Milnor's K-theory plays an important role.

In 1992 he received the prize of the St. Petersburg Mathematical Society.

He is one of the few prominent mathematicians who intensively with the theory building of inter-universal Teichmüller theory of Shinichi Mochizuki apart translated, and which he considers a promising development. He organized two workshops on this (2015 in Oxford and 2016 at the RIMS in Kyoto) and published a review article. This was also funded by the Nottingham-Oxford-EPSRC Program Grant Symmetries and Correspondences (totaling £ 2.3 million), of which Fesenko is a senior scientist (alongside Nigel Hitchin , Boris Zilber , Minhyong Kim , Kobi Kremnitzer ) .

Fonts

  • with SV Vostokov Local fields and their extensions. A constructive approach , American Mathematical Society 1993, 2nd edition 2002
  • with Masato Kurihara (editor) Invitation to higher local fields , Geometry and Topology Monographs 3, University of Warwick 2000, Online
  • Abelian extensions of complete discrete valuation fields , in Sinnou David (Editor) Number Theory. Seminaire de Theory des Nombres de Paris 1993/94 , London Mathematical Society Lecture Note Series, Cambridge Univ. Press 1996, pp. 47-74.
  • Complete discrete valuation fields k Abelian local class field theories , in M. Hazewinkel (editor) Handbook of Algebra , Volume 1, Elsevier 1996, pp. 221-268.
  • Class field theory of multidimensional local fields of characteristic 0, with the residue field of positive characteristic m, St. Petersburg Mathematical Journal, Volume 3, 1992, pp. 649-678
  • Multidimensional local class field theory , Part 1, Acad. Sci. SSR Docl. Math., Volume 43, 1991, pp. 674-677 (English), Docl. Akad. Nauka SSSR, Volume 318, 1991, pp. 47-50 (Russian), Part 2 Algebra i Analiz, Volume 3, Issue 5, 1991, pp. 168-189 (Russian), St. Petersburg Math. J., Volume 3, 1992, pp. 1103-1126 (English)
  • Abelian local p-class field theory , Mathematische Annalen, Volume 301, 1995, pp. 561-586.
  • Local class field theory: perfect residue field case , Izv. Akad. Nauka, Ser. Math., Vol. 43, 1994, pp. 65-81.
  • On general local reciprocity maps , Journal for pure and applied mathematics, Volume 473, 1996, pp. 207–222.
  • Nonabelian local reciprocity maps , in Katsuya Miyake, Nihon Suggakai (editor) Class Field Theory - Its Centenary and Prospect , Advanced Studies in Pure Mathematics 30, Mathematical Society of Japan, 2001, pp. 63-78
  • Adelic approach to the zeta function of arithmetic schemes in dimension two , Moscow Mathematical Journal, Volume 8, 2008, pp. 273-317.
  • with M. Suzuki, G. Ricotta Mean-periodicity and zeta functions , Annales de L'Institut Fourier, Volume 62, 2012, pp. 1819-1887.
  • Analysis on arithmetic schemes , Part 1, Documenta Mathematica, Kato 50th Birthday Volume, pp. 261-284, Part 2: Journal of K-theory, Volume 5, 2010, pp. 437-557.

Web links

Individual evidence

  1. ↑ Iwan Borissowitsch Fessenko in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ Fesenko, Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki, Europ. J. Math., Volume 1, 2015, pp. 405-440.
  3. ↑ Fesenko, Fukugen , Inference: International Review of Science, 2, 2016
  4. ↑ EPSRC Program Grant Symmetries and Correspondences: intra-disciplinary developments and applications 2015-2021
personal data
SURNAME Fessenko, Ivan Borisovich
ALTERNATIVE NAMES Фесенко, Иван Борисович (Russian spelling); Fesenko, Ivan (English transcription)
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH 1962