According to Mochizuki, it is "an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve".
[1] Mochizuki made his work public in August 2012 with none of the fanfare that typically accompanies major advances, posting the papers only to his institution's preprint server and his website, and making no announcement to colleagues.
[2][3][4] Soon after, the papers were picked up by Akio Tamagawa and Ivan Fesenko and the mathematical community at large was made aware of the claims to have proven the abc conjecture.
[12] In March 2018, Peter Scholze and Jakob Stix visited Kyoto University for five days of discussions with Mochizuki and Yuichiro Hoshi; while this did not resolve the differences, it brought into focus where the difficulties lay.
On one hand, Hodge theaters generalize such classical objects in number theory as the adeles and ideles in relation to their global elements.
[25] One issue with Mochizuki's arguments, which he acknowledges, is that it does not seem possible to get intermediate results in his claimed proof of the abc conjecture using IUT.
In other words, there is no smaller subset of his arguments more easily amenable to an analysis by outside experts, which would yield a new result in Diophantine geometries.