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URLﾘﾝｸ(www.yurinsha.com)
Mochizuki Shinichi
Inter-universal Teichmuller Theory I - IV
Special Issue of PRIMS, Vol. 57, No. 1/2
Softcover
Price: \ 13,500.
Pages: 723
Published: March 2021
Copyright: 2021 EMS
The present paper is the first in a series of four papers, the goal of which is to establish an arithmetic version of Teichmuller theory for number fields equipped with an elliptic curve ? which we refer to as "inter-universal Teichmuller theory" ? by applying the theory of semi-graphs of anabelioids,
Frobenioids, the etale theta function, and log-shells developed in earlier papers by the author. We begin by fixing what we call "initial Θ-data", which consists of an elliptic curve EF over a number field FF, and a prime number l?5l?5, as well as some other technical data satisfying certain technical properties. This data determines various hyperbolic orbicurves that are related via finite etale coverings to the once-punctured elliptic curve XF determined by EF. These finite etale coverings admit various symmetry properties arising from the additive and multiplicative structures on the ring Fl=Z/lZ acting on the ll-torsion points of the elliptic curve. We then construct "Θ±ellNF-Hodge theaters" associated to the given Θ- data. These Θ±ellNF-Hodge theaters may be thought of as miniature models of conventional scheme theory in which the two underlying combinatorial dimensions of a number field ? which may be thought of as corresponding to the additive and multiplicative structures of a ring or, alternatively, to the group of units and value group of a local field associated to the number field ? are, in some sense, "dismantled" or "disentangled" from one another.
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