Public

ABC Day 1.

Zhang gave a nice talk about function field Szpiro (not directly related to Mochizuki's work).

Kühn and Javanpeykar spoke on Mochizuki's earlier paper "Arithmetic Elliptic Curves in General Position". This paper essentially reduces abc (and Vojta's conjecture for curves) to a special case of abc where the numbers satisfy some congruence conditions (expressed as adelic restrictions) using Belyi maps. This seems like normal mathematics and people seemed generally happy with it.

Hoshi gave two talks (nicely delivered) explaining some concepts from Mochizuki's IUT. There were a number of words expressing standard mathematical ideas (algorithm, holomorphic,...) used in non-standard ways and non-standard names for standard concepts ("coric" = surjective, "multiradial" = not injective,...). I guess it will be helpful later but it was frustrating. He also showed how to recover various structures associated with local fields from their absolute Galois group which were variants of standard stuff. Lots of talk about how later one will compute some power of the Tate parameter q of an elliptic curve at a bad place as if it were q itself and then compare with q to get a bound. That seems to be the goal but any concrete details will come later, apparently.

Tomorrow we start with Mochizuki on Skype!

Zhang gave a nice talk about function field Szpiro (not directly related to Mochizuki's work).

Kühn and Javanpeykar spoke on Mochizuki's earlier paper "Arithmetic Elliptic Curves in General Position". This paper essentially reduces abc (and Vojta's conjecture for curves) to a special case of abc where the numbers satisfy some congruence conditions (expressed as adelic restrictions) using Belyi maps. This seems like normal mathematics and people seemed generally happy with it.

Hoshi gave two talks (nicely delivered) explaining some concepts from Mochizuki's IUT. There were a number of words expressing standard mathematical ideas (algorithm, holomorphic,...) used in non-standard ways and non-standard names for standard concepts ("coric" = surjective, "multiradial" = not injective,...). I guess it will be helpful later but it was frustrating. He also showed how to recover various structures associated with local fields from their absolute Galois group which were variants of standard stuff. Lots of talk about how later one will compute some power of the Tate parameter q of an elliptic curve at a bad place as if it were q itself and then compare with q to get a bound. That seems to be the goal but any concrete details will come later, apparently.

Tomorrow we start with Mochizuki on Skype!

- Can you say a bit more about recovering "various structures associated with local fields from their absolute Galois group which were variants of standard stuff" ? Are you referring to Mochizuki's theorem that a local field can be recovered from its absolute Galois group endowed with the ramification filtration ? Or is there something more to it ?Dec 7, 2015
- The particular result that was stated was that if G was the absolute Galois group of a local field and M was a monoid with G action isomorphic to A-{0} (A the ring of integers of the field), then one could produce a specific isomorphism from M to A-{0}. Similarly with A-{0} replaced by units. The result only concerned the multiplicative structure of A-{0}, so it was easier than recovering the whole field and could be done with Kummer theory.Dec 8, 2015