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The editors of this volume wish to express to Kazuya Kato their gratitude and admiration for his seminal contributions to arithmetic algebraic geometry and the deep influence he has been exerting in this area for over twenty years through his students and collaborators throughout the world.
S. Bloch, I. Fesenko, L. Illusie, M. Kurihara, S. Saito, T. Saito, P. Schneider
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