Arithmetic of hyperbolic algebraic curves related to arithmetic fundamental groups

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04780
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: Hoshi Yuichiro 京都大学, 数理解析研究所, 准教授 (50456761)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 双曲的代数曲線 / 数論的基本群 / 遠アーベル幾何学 / p進Teichmuller理論 / 休眠乍 / 等分点 / 巾零通常固有束 / 射影構造

Outline of Final Research Achievements

(1) I proved uniqueness of dormant opers of rank p-1 on a projective hyperbolic curves in characteristic p. (2) I studied torsion points on algebraic curves that have good reduction over absolutely unramified bases. (3) I obtained a certain categorical representation of log schemes. (4) I obtained categorical characterizations of isomorphism classes of local fields. (5) I established a pro-p criterion for good reduction of ordinary curves. (6) I solved the anabelian conjecture for moduli spaces of elliptic curves equipped with additional data. (7) I developed combinatorial anabelian geometry. (8) I gave a characterization of supersingular divisors of nilpotent ordinary indigenous bundles. (9) I established a certain positive characteristic analogue of theory of projective structures on Riemann surfaces. (10) I studied the anabelian geometry of local fields.

Free Research Field

数物系科学