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- Inter-universal_Teichmüller_theory abstract "In mathematics, inter-universal Teichmüller theory (IUT) is an arithmetic version of Teichmüller theory for number fields endowed with an elliptic curve, introduced by Shinichi Mochizuki (2012a, 2012b, 2012c, 2012d). 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' . . . [defined 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'."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 (Mochizuki 2012d) 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 a two digital number of new concepts 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. Mochizuki (2013b) and Mochizuki (2014) 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 Bejing in July 2015. A workshop of Clay Mathematics Institute on the theory of Mochizuki is scheduled for December 2015, IUT-CMI (2015).".
- Inter-universal_Teichmüller_theory wikiPageExternalLink IUTeich%20Verification%20Report%202013-12.pdf.
- Inter-universal_Teichmüller_theory wikiPageExternalLink IUTeich%20Verification%20Report%202014-12.pdf.
- Inter-universal_Teichmüller_theory wikiPageExternalLink Inter-universal%20Teichmuller%20Theory%20IV%20(comments).pdf.
- Inter-universal_Teichmüller_theory wikiPageExternalLink symcor.iut.html.
- Inter-universal_Teichmüller_theory wikiPageExternalLink 107279.
- Inter-universal_Teichmüller_theory wikiPageExternalLink index.php?title=ABC_conjecture.
- Inter-universal_Teichmüller_theory wikiPageExternalLink 2015-03%20IUTeich%20Program%20(English).pdf.
- Inter-universal_Teichmüller_theory wikiPageExternalLink papers-english.html.
- Inter-universal_Teichmüller_theory wikiPageExternalLink notesoniut.pdf.
- Inter-universal_Teichmüller_theory wikiPageExternalLink symcor.conf.html.
- Inter-universal_Teichmüller_theory wikiPageID "36968172".
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- Inter-universal_Teichmüller_theory wikiPageWikiLink Abc_conjecture.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Algebraic_number_field.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Category:Algebraic_geometry.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Category:Number_theory.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Clay_Mathematics_Institute.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Diophantine_geometry.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Elliptic_curve.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Fesenko.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Fiber_functor.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Galois_group.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Ivan_Fesenko.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Mathematics.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Number_field.
- Inter-universal_Teichmüller_theory wikiPageWikiLink P-adic_Teichmüller_theory.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Research_Institute_for_Mathematical_Sciences.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Set_theory.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Szpiro_conjecture.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Szpiros_conjecture.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Teichmüller_space.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Teichmüller_theory.
- Inter-universal_Teichmüller_theory wikiPageWikiLink Vojtas_conjecture.
- Inter-universal_Teichmüller_theory wikiPageWikiLinkText "IU Theory".
- Inter-universal_Teichmüller_theory wikiPageWikiLinkText "Inter-universal Teichmüller theory".
- Inter-universal_Teichmüller_theory wikiPageWikiLinkText "inter-universal Teichmüller theory".
- Inter-universal_Teichmüller_theory authorlink "Shinichi Mochizuki".
- Inter-universal_Teichmüller_theory first "Shinichi".
- Inter-universal_Teichmüller_theory hasPhotoCollection Inter-universal_Teichmüller_theory.
- Inter-universal_Teichmüller_theory last "Mochizuki".
- Inter-universal_Teichmüller_theory wikiPageUsesTemplate Template:Citation.
- Inter-universal_Teichmüller_theory wikiPageUsesTemplate Template:Harv.
- Inter-universal_Teichmüller_theory wikiPageUsesTemplate Template:Harvs.
- Inter-universal_Teichmüller_theory wikiPageUsesTemplate Template:Reflist.
- Inter-universal_Teichmüller_theory year "1.738368E8".
- Inter-universal_Teichmüller_theory year "2012".
- Inter-universal_Teichmüller_theory subject Category:Algebraic_geometry.
- Inter-universal_Teichmüller_theory subject Category:Number_theory.
- Inter-universal_Teichmüller_theory comment "In mathematics, inter-universal Teichmüller theory (IUT) is an arithmetic version of Teichmüller theory for number fields endowed with an elliptic curve, introduced by Shinichi Mochizuki (2012a, 2012b, 2012c, 2012d). Several previously developed and published theories by Mochizuki are related in various ways to IUT.".
- Inter-universal_Teichmüller_theory label "Inter-universal Teichmüller theory".
- Inter-universal_Teichmüller_theory sameAs m.0m0kv0j.
- Inter-universal_Teichmüller_theory sameAs Q19597596.
- Inter-universal_Teichmüller_theory sameAs Q19597596.
- Inter-universal_Teichmüller_theory wasDerivedFrom Inter-universal_Teichmüller_theory?oldid=680193440.
- Inter-universal_Teichmüller_theory isPrimaryTopicOf Inter-universal_Teichmüller_theory.