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In mathematics, inter-universal Teichmüller theory (IUT) is an arithmetic version of Teichmüller theory for number fields endowed with an elliptic curve, introduced by . 〔.〕〔.〕〔.〕〔.〕〔.〕 Several previously developed and published theories by Mochizuki are related in various ways to IUT. They include his p-adic Teichmüller theory, his Hodge-Arakelov theory, his mono-anabelian geometry and his etale-theta functions theory. Mochizuki explains the name as follows: "in this sort of a situation, one must work with the Galois groups involved as abstract topological groups, which are not equipped with the 'labeling apparatus' . . . (as ) the ''universe'' that gives rise to the model of set theory that underlies the codomain of the fiber functor determined by such a basepoint. It is for this reason that we refer to this aspect of the theory by the term '' Inter-universal Teichmüller theory provides an explicit description of the arithmetic Teichmüller deformations of a number field endowed with an elliptic curve. The main theorems include two inequalities on the log-volume change associated to appropriately chosen deformations. The theorems imply a proof of several equivalent fundamental conjectures in Diophantine geometry, including the abc conjecture over any number field, the strong Szpiro conjecture over any number field, and part of the Vojta's conjecture for the case of hyperbolic curves over any number field. IUT extends substantially the scope of arithmetic geometry. The theory is complex, includes many new concepts in mathematics, and requires substantial efforts to understand. During different stages of study and verification of the theory, V. Dimitrov and A. Venkatesh, G. Yamashita, Yu. Hoshi, M. Saidi, I. Fesenko have made and asked hundreds of comments and questions, all of which have been addressed by the author. and gave a summary of progress in verifying his work; the survey provides an external perspective. A workshop on IUT was held at RIMS in March 2015 and in Beijing in July 2015. A workshop of Clay Mathematics Institute on the theory of Mochizuki is scheduled for December 2015, . ==References== * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Inter-universal Teichmüller theory」の詳細全文を読む スポンサード リンク
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