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Where does the wonder of numbers come from?Finding new arithmetic phenomena via generalized motives 
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In the study of mathematics, we often find mysterious connections between two seemingly unrelated objects and phenomena. The aim of this research is to understand how these mysterious connections appear, by using the theory of generalized motives, which was developed in my previous research. We can study numbers by observing a type of shape called algebraic varieties. The theory of generalized motives enables us to continuously observe algebraic varieties from various points of view. The shapes of algebraic varieties observed from different points of view appear to be different, but they can be connected through this continuous observation. By using the theory of generalized motives, we can systematically connect seemingly different objects without relying on random luck. We anticipate that this study will accelerate the research on number theory, which underpins human activity everywhere.
[1] B. Kahn, H. Miyazaki, S. Saito, T. Yamazaki, “Motives with modulus, III,” Annals of K-theory (to appear).
[2] B. Kahn, H. Miyazaki, S. Saito, T. Yamazaki, “Motives with modulus, II,” Épijournal de Géométrie Algébrique, Vol. 5, epiga:7115, 2021.
[3] B. Kahn, H. Miyazaki, S. Saito, T. Yamazaki, “Motives with modulus, I,” Épijournal de Géométrie Algébrique, Vol. 5, epiga:7114, 2021.
[4] B. Kahn, H. Miyazaki, “Topologies on schemes and modulus pairs,” Nagoya Mathematical Journal, Vol. 244, pp. 283–313, 2021.
[5] H. Miyazaki, “Nisnevich topology with modulus,” Annals of K-theory, Vol. 5, pp. 581–604, 2019.
Hiroyasu Miyazaki / Institute for Fundamental Mathematics
Email: cs-openhouse-ml@hco.ntt.co.jp