| Tsuzuki Nobuo , Professor |
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Research field
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Arithmetic geometry and number theory
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Research of interest |
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Arithmetic geometry is a field of mathematics in which one studies arithmetic varieties defined by algebraic equations over a small fields as the field of rational numbers, finite fields and the fields of p-adic numbers. When one considers various types of ``cohomology", one would have local systems, e.g., Hodge structures, Galois representations, and F-isocrystals. By the study of local systems, one can know arithmetic properties of varieties. I am working on cohomologies defined by using p-adic analytic differential forms on arithmetic varieties. Recently, its framework is becoming more completed than before. Now I would like to apply the theory to study arithmetic varieties and their number theoretic applications.
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Advice on Research |
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I hope students who like mathematics very much. Initially you might have a hard time, but the joy you can get should be immense when you will understand something. When you study mathematics, please try to use your hands and move them to make examples by yourself. It should help you understand their concepts deeply.
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Some of titles of master’s theses that have been advised |
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- “A study on modular degrees of elliptic curves”
- “A study on the properties of multiple zeta values and their relations”
- “Conditions under which the 2-part of class groups of imaginary quadratic fields”
- “Imaginary measure of various numbers”
- “Fourier coefficients of Ikeda lifts of degree 4”
- “Primality test algorithms and their times of motions”
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Faculty Member