Study at TCU


Official Title Associate Professor
Affiliation Natural Sciences, Science and Engineering
Profile My research area is arithmetic geometry. I worked on ramification theory and integral p-adic Hodge theory, and recently I am more interested in congruence of modular forms. For automorphic forms on reductive algebraic groups over number fields, we have highly developped theory of p-adically analytic families of automorphic forms, including eigenvarieties. I am studying geometric properties of eigenvarieties and its arithmetic applications. On the other hand, though the construction of analytic families fails for Drinfeld modular forms, a function field analogue of elliptic modular forms, interesting phenomena on v-adic properties of Drinfeld modular forms are discovered via numerical computation. I am also working on establishing the theory of v-adic congruences of Drinfeld modular forms.
Research Field(Keyword & Summary)
  1. slopes of Drinfeld modular forms

    Slope is the normalized v-adic valuation of U_v-operator acting on Drinfeld modular forms. Numerical computation indicates that there should be mysterious structures surrounding slopes, of which we do not know the origin. The aim of this study is to reveal the structure osf slopes of Drinfeld modular forms with v-adic geometric method.

Representative Papers
  1. (1) S. Hattori: P-adic continuous families of Drinfeld eigenforms of finite slope, Advances in Mathematics 380 (2021), 107594.
  2. (2) S. Hattori: Dimension variation of Gouvea-Mazur type for Drinfeld cuspforms of level Γ1(t), International Mathematics Research Notices (2021), no. 3, 2389--2402.
  3. (3) S. Hattori: Duality of Drinfeld modules and P-adic properties of Drinfeld modular forms, Journal of the London Mathematical Society 103 (2021), no. 1, 35--70.
  4. (4) S. Hattori and J. Newton: Irreducible components of the eigencurve of finite degree are finite over the weight space, Journal fur die reine und angewandte Mathematik 763 (2020), 251--269.
  5. (5) S. Hattori: Ramification theory and perfectoid spaces, Compositio Mathematica 150 (2014), no. 5, 798--834.
Grant-in-Aid for Scientific Research Support: Japan Society for Promotion of Science (JSPS)
Recruitment of research assistant(s) No
Affiliated academic society (Membership type) The Mathematical Society of Japan
Education Field (Undergraduate level) linear algebra, calculus, vector calculus, complex analysis
Education Field (Graduate level) elliptic curves and modular forms