SAITO, Shuji

Title
Professor
Field
arithmetic geometry, algebraic geometry, algebraic K-thoery
Research interests
Higher dimensional class field theory, algebraic cycles, motives, motivic cohomology
Current research

There are mainly three different topics: Higher dimensional class field theory, theory of motives, analytic K-theory of rigid spaces.

Notice for the students

For sutudents who wish to study under my supervision in the master course, it is absolutely necessary to understand the standard subjects in algebra such as groups, rings, fields, modules, Galois theory. It is also necessary to learn scheme theory, homological algebra, sheaf theory. It is also desirable to study arithmetic of local fields and number fields. In research in arithmetic geometry, wide range of knowledge is required and much effort is demanded to reach to a front line of reserach. Have a big dream but not forget honest labor of computations is also indispensable in mathmatical research.

Selected publications
  1. S. Saito and K. Sato, A finite theorem for zero-cycles over p-adic fields, Annals of Mathematics 172 (2010), 593--639
  2. S. Saito, Motives and Filtrations on Chow groups, Invent. Math. 125 (1996), 149--196
  3. S. Saito, Unramified class field theory of arithmetical schemes, Ann. of Math. 121 (1985), 251--281 )
  4. M. Kerz and S. Saito, Chow group of 0-cycles with modulus and higher dimensional class field theory, Duke Math. J. 165 , no. 15 (2016), 2811--2897
  5. M. Kerz and S. Saito, Cohomological Hasse principle and motivic cohomology of arithmetic schemes, Publ. Math. IHES 115 (2012), 123--183
  6. S. Saito and K. Sato, Zero-cycles on varieties over p-adic fields and Brauer groups, Ann. Sci. Ecole Norm. Sup. 47 (2014), 505--537

Memberships, activities and

Awards

The Spring Prize of the Mathematical Society of Japan (1996)

Alexander von Humboldt research award (2016)