Investigation of degenerations and uniformizations by means of rigid geometry

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400050
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Tokyo Institute of Technology (2015-2016); Kumamoto University (2014)
• Principal Investigator: Kato Fumiharu 東京工業大学, 理学院, 教授 (50294880)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: リジッド幾何学

Outline of Final Research Achievements

(1) A totally new p-adic uniformization with torsion in dimension two, which gives rise to a fake projective plane which is, however, non-isomorphic to the Mumford's one, has been observed for the first time, in the course of our enduring investigation for higher dimensional non-archimedean "orbifold uniformization", viz., uniformization with torsion elements.
(2) The full-scale theorization of the so-called "Henselian rigid geometry" has been embarked, probably for the first time in this field of mathematical researches, as a new conceptualization of most modern algebro-geometric and rigid-analytic hybrid spaces, which will, expectedly, enhance the arithmetico- and algebro-geometric aspects of the classical rigid geometry.

Free Research Field

代数幾何学