Tsuzuki Nobuo , Professor 
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Research field



Arithmetic geometry and number theory


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Research of interest 


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 padic numbers. When one considers various types of ``cohomology", one would have local systems, e.g., Hodge structures, Galois representations, and Fisocrystals. By the study of local systems, one can know arithmetic properties of varieties. I am working on cohomologies defined by using padic 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 

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 masterfs theses that have been advised 

 gA study on modular degrees of elliptic curvesh
 gA study on the properties of multiple zeta values and their relationsh
 gConditions under which the 2part of class groups of imaginary quadratic fieldsh
 gImaginary measure of various numbersh
 gFourier coefficients of Ikeda lifts of degree 4h
 gPrimality test algorithms and their times of motionsh
