|DATE||July 23 (Mon), 2018|
|INSTITUTE||RIMS(Research Institute for Mathematical Sciences)|
|TITLE||Introduction to Interuniversal Teichmueller Theory I|
|ABSTRACT||These talks are aimed to explain the main result and some crucial technical points of the IUT theory of Shinichi Mochizuki. Time permitting, we will sketch a proof of the ABC/Vojta conjecture, as an application of IUT theory.
In IUT, one starts with a suitable elliptic curve E and a prime number l (among other technical data), and studies such a collection of data via certain hyperbolic curves, which link to theta functions via anabelian geometry. A variety of geometric and arithmetic information about the elliptic curve and theta function is recorded in the so-called Hodge theater, which carries two kinds of symmetries associated to a fixed quotient of l-torsions of E. The first symmetry will be applied to copies of the field of moduli of E, while the second assures that the conjugacies of local Galois groups on various values of theta function are synchronized. These theta values and the number field will determine the so-called theta-pilot object, whose construction relies on everything aforementioned.
The main construction of IUT is the so-called multiradial (i.e. invariant under changes of ring structures) representation of the theta-pilot object. The construction of such a representation can only be achieved under the indeterminacies/equivalences (Ind1, 2, 3), which are responsible for the final inequality on arithmetic degrees.