Tamagawa received his PhD in 1954 at the University of Tokyo under Shōkichi Iyanaga.
Tamagawa was a visiting scholar at the Institute for Advanced Study in 1955/6, 1958, and 1970.
These measures play an essential role in conjectures on arithmetic algebraic geometry, such as those of Spencer Bloch and Kazuya Kato.
Tamagawa's doctoral students included Doris Schattschneider and Audrey Terras.
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