SAITO Takeshi

Arithmetic geometry
Research interests

Galois representations, ramification

Current research

Arithmetic geometry studies algebraic varieties defined over arithmetic fields or rings including Q, Q_p Z, etc. The main object of study is l-adic Galois representations of global and local field defined as etale cohomology of varieties.

Selected publications
  1. Ramification theory for varieties over a local field, with Kazuya Kato,
    Publications Mathematiques, IHES. 117, (2013), 1-178

  2. The characteristic class and ramification of an l-adic etale sheaf, with Ahmed Abbes,
    Inventiones Mathematicae 168 No. 3 (2007) 567-612

  3. On the conductor formula of Bloch, with Kazuya KATO,
    Publications Mathematiques, IHES 100, (2004), 5-151.

  4. Ramification of local fields with imperfect residue fields, with Ahmed ABBES,
    American Journal of Mathematics, 124.5 (2002), 879-920

  5. Modular forms and p-adic Hodge theory,
    Inventiones Math. 129 (1997) 607-620


Number theory 1, Fermat's dream
(with K. Kato, N. Kurokawa, translated by M. Kuwata) (2000)

Number theory 2, Introduction to Class Field Theory
(with K. Kato, N. Kurokawa, translated by M. Kuwata) (2011)

Number theory 3, Iwasawa Theory and Modular Forms
(with N. Kurokawa, M. Kurihara translated by M. Kuwata) (2012)


awards and


Mathematical Society of Japan

Algebra prize 1998.9,

Spring prize of Math. Soc. Japan 2001.3

Documenta DMV, Japanese Journal of Mathematics (editor).