これ、いいね！ https://www.kurims.kyoto-u.ac.jp/~motizuki/ExpHorizIUT21/WS4/ExpHorizIUT21-IUTSummit-notes.html Inter-universal Teichmuller Theory (IUT) Summit 2021, RIMS workshop, September 7 - September 10 2021 https://www.kurims.kyoto-u.ac.jp/~motizuki/ExpHorizIUT21/WS4/documents/Porowski%20-%20Overview%20of%20IUT.pdf Overview of some of aspects IUT Wojciech Porowski September 2021
P3 Structure of the theory How to briefly summarise the structure of IUT? Roughly speaking, the main result of the theory is a construction of certain group-theoretic algorithm and description of its properties. In particular, this algorithm is compatible with Kummer-theories (up to certain indeterminacies), which link Frobenius-like structures with its ´etale-like counterparts and with the Θ-link. We will try to discuss some of the expressions appearing above and explain how they fit into the IUT theory.
P5 Algorithms in IUT We will not attempt to give a precise definition of a ”group theoretical algorithm”. However, we note here the following important point: in IUT, in various statements concerning the existence of a particular group theoretic algorithm, the construction of this algorithm itself constitutes an important of the statement. Informally, one could say that the way we construct an object is as important as the (isomorphism class) of the considered object. Let us also recall that groups that we use in the theory to construct various objects are either (´etale or tempered) fundamental groups of (orbi-)curves or absolute Galois groups of fields (local or global)
