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- Inter-universal_Teichmüller_theory abstract "In mathematics, inter-universal Teichmüller theory is an arithmetic version of Teichmüller theory for number fields with an elliptic curve, introduced by Shinichi Mochizuki (2012a, 2012b, 2012c, 2012d) as an extension of his work on p-adic Teichmüller theory. The main theorem of inter-universal Teichmüller theory gives an explicit description of the arithmetic Teichmüller deformations of a number field with an elliptic curve. The paper (Mochizuki 2012d) claims to use the main theorem to give a proof of several outstanding conjectures in diophantine geometry, including the abc conjecture, the Szpiro conjecture, and part of the Vojta conjecture for the case of hyperbolic curves. The proofs are unusually difficult to understand, and as of 2014 there is no consensus on whether or not they are correct. In September 2012, Vesselin Dimitrov and Akshay Venkatesh found some problems with theorem 1.10 of Mochizuki's 4th paper, and Mochizuki (2012e) then wrote some comments agreeing that there was a small error in his papers and explaining how to fix it. Mochizuki (2013b) gave a summary of progress in verifying his work. 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 wikiPageID "36968172".
- Inter-universal_Teichmüller_theory wikiPageRevisionID "606205809".
- Inter-universal_Teichmüller_theory authorlink "Shinichi Mochizuki".
- Inter-universal_Teichmüller_theory first "Shinichi".
- Inter-universal_Teichmüller_theory last "Mochizuki".
- 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 is an arithmetic version of Teichmüller theory for number fields with an elliptic curve, introduced by Shinichi Mochizuki (2012a, 2012b, 2012c, 2012d) as an extension of his work on p-adic Teichmüller theory. The main theorem of inter-universal Teichmüller theory gives an explicit description of the arithmetic Teichmüller deformations of a number field with an elliptic curve.".
- Inter-universal_Teichmüller_theory label "Inter-universal Teichmüller theory".
- Inter-universal_Teichmüller_theory label "宇宙際タイヒミュラー理論".
- Inter-universal_Teichmüller_theory sameAs Inter-universal_Teichm%C3%BCller_theory.
- Inter-universal_Teichmüller_theory sameAs 宇宙際タイヒミュラー理論.
- Inter-universal_Teichmüller_theory sameAs Q6044776.
- Inter-universal_Teichmüller_theory sameAs Q6044776.
- Inter-universal_Teichmüller_theory wasDerivedFrom Inter-universal_Teichmüller_theory?oldid=606205809.