Toshihisa Urahigashi

A local non-containment in Step (v) of IUT IV, Theorem 1.10

Step (v) of the proof of Theorem 1.10 in Mochizuki's Inter-universal Teichmüller theory IV bounds, for each tuple of places, the log-volume of the corresponding component of the holomorphic hull of the union of possible images of a Θ-pilot object defined in Corollary 3.12 of the...

A local non-containment in Step (v) of IUT IV, Theorem 1.10

Step (v) of the proof of Theorem 1.10 in Mochizuki's Inter-universal Teichmüller theory IV bounds, for each tuple of places, the log-volume of the corresponding component of the holomorphic hull of the union of possible images of a Θ-pilot object defined in Corollary 3.12 of the...

An initial Θ-datum over an imaginary quadratic field, and numerical values of the local quantities of inter-universal Teichmüller theory IV (A second report)

Version note. The first report has withdrawn, in its version 0.1.7, the source application under which the values 8/7 and 88/7 were read as an incompatibility with IUT IV; see that report's §7 for the locators and for a proposition limiting the scope of the withdrawal. No stateme...

Split bad primes and the tuple structure of inter-universal Teichmüller theory: what the source states, and what follows (A fourth report)

Version note. The first report has withdrawn, in its version 0.1.7, the source application under which the values 8/7 and 88/7 were read as an incompatibility with IUT IV; see that report's §7 for the locators and for a proposition limiting the scope of the withdrawal. No stateme...

An initial Θ-datum over an imaginary quadratic field, and numerical values of the local quantities of inter-universal Teichmüller theory IV (A second report)

Version note. The first report has withdrawn, in its version 0.1.7, the source application under which the values 8/7 and 88/7 were read as an incompatibility with IUT IV; see that report's §7 for the locators and for a proposition limiting the scope of the withdrawal. No stateme...

Split bad primes and the tuple structure of inter-universal Teichmüller theory: what the source states, and what follows (A fourth report)

Version note. The first report has withdrawn, in its version 0.1.7, the source application under which the values 8/7 and 88/7 were read as an incompatibility with IUT IV; see that report's §7 for the locators and for a proposition limiting the scope of the withdrawal. No stateme...

The cost of each distinction in the local computations of inter-universal Teichmüller theory IV (A third report)

A third report in the series begun by 10.5281/zenodo.22537342 and continued in 10.5281/zenodo.22601333. The local estimates of Mochizuki, Inter-universal Teichmüller Theory IV, §1, are assembled from several steps that the source keeps apart: a p-primary torsion term, a normaliza...

An initial Θ-datum over an imaginary quadratic field, and numerical values of the local quantities of inter-universal Teichmüller theory IV (A second report)

A second report in the series begun by 10.5281/zenodo.22537342. We exhibit an initial Θ-datum in the sense of Mochizuki, Inter-universal Teichmüller Theory I, Definition 3.1, whose field of moduli is the imaginary quadratic field Q(i): the curve E0: y² = x(x−1)(x−a) with a = (10+...

An explicit initial Θ-datum with mixed reduction at a split prime

We exhibit an explicit initial Θ-datum in the sense of Mochizuki, IUT I, Definition 3.1: an elliptic curve in Legendre form over Q(√5) with ℓ = 7, for which the rational prime 211 splits in the field of moduli, so that one place of multiplicative and one place of good reduction l...

An initial Θ-datum over an imaginary quadratic field, and numerical values of the local quantities of inter-universal Teichmüller theory IV (A second report)

A second report in the series begun by 10.5281/zenodo.22537342. We exhibit an initial Θ-datum in the sense of Mochizuki, Inter-universal Teichmüller Theory I, Definition 3.1, whose field of moduli is the imaginary quadratic field Q(i): the curve E0: y² = x(x−1)(x−a) with a = (10+...

An explicit initial Θ-datum with mixed reduction at a split prime

We exhibit an explicit initial Θ-datum in the sense of Mochizuki, IUT I, Definition 3.1: an elliptic curve in Legendre form over Q(√5) with ℓ = 7, for which the rational prime 211 splits in the field of moduli, so that one place of multiplicative and one place of good reduction l...

An explicit initial Θ-datum with mixed reduction at a split prime

We exhibit an explicit initial Θ-datum in the sense of Mochizuki, IUT I, Definition 3.1: an elliptic curve in Legendre form over Q(√5) with ℓ = 7, for which the rational prime 211 splits in the field of moduli, so that one place of multiplicative and one place of good reduction l...