2009 Fiscal Year Final Research Report

Model Theory of analytic structures and quasi-minimal fields

Research Project

Project/Area Number	19540146
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	General mathematics (including Probability theory/Statistical mathematics)
Research Institution	Tokai University
Principal Investigator	ITAI Masanori Tokai University, 理学部, 教授 (80266361)
Project Period (FY)	2007 – 2009
Keywords	モデル理論 / 解析的構造 / 擬極小体 / 解析的ザリスキー幾何
Research Abstract	There are two results : the first one is concerning "Chow's Theorem". This famous theorem in algebraic geometry claims that any analytic variety in projective space is in fact algebraically defined. Dr. Peatfield and Prof. Zilber at Oxford University had proved a Chow type theorem in an analytic Zariski structure situation. We proved a generalization of their theorem. The second one is to apply Richardson's Theorem to algebraically closed fields equipped with a pseudo-exponentiation called Kex. Richardson's theorem gives irreducible decompositions of the zero sets to a system of algebraic-exponential equations. An algebraic-exponential equation is an algebraic equation allowing finitely may exponential functions to appear in it. We proved that the same statement holds in Kex.

(7 results)