/sci/ - Science & Math

>Mochizuki's anabelian variation of ring structures and formal groups
>Kirti Joshi
>(Submitted on 17 Jun 2019)

>I show that there is a universal formal group (over a suitable (non-zero) ring) which is equipped with an action of the multiplicative monoid [math]\mathcal{O}^\triangleright[/math] of non-zero elements of the ring of integers of a p-adic field. Lubin-Tate formal groups also arise from this universal formal group. If two p-adic fields have isomorphic multiplicative monoids [math]\mathcal{O}^\triangleright[/math] then the additive structure of one arises from that of the other by means of this universal formal group law (in a suitable manner). In particular if two p-adic fields have isomorphic absolute Galois groups then it is well-known that the two respective monoids [math]\mathcal{O}^\triangleright[/math] are isomorphic and so this construction can be applied to such p-adic fields. In this sense this universal formal group law provides a single additive structure which binds together p-adic fields whose absolute Galois groups are isomorphic (this anabelian variation of ring structure is studied and used extensively by Shinichi Mochizuki). In particular one obtains a universal (additive) expression for any non-zero p-adic integer (in a given p-adic field) which is independent of the ring structure of the p-adic field (this is also inspired by Mochizuki's results).

This is now an IUT thread.

>>7949649
An ellipse.

>>7425994

This is my kind of problem....

I don't know that feel bro