>>433
>望月IUTで、楕円曲線が重要だというのとは、両立すると思う

補足
望月先生の米 Berkeley Colloquium (Zoom) のPDFが下記
”elliptic curves”、”Theta function”が出てきます
正直、私には、”お経”ですけどね（＾＾；

http://www.kurims.kyoto-u.ac.jp/~motizuki/2020-11%20Classical%20roots%20of%20IUT.pdf
[16] Classical Roots of Inter-universal Teichmuller Theory (Berkeley Colloquium (Zoom) 2020年11月).
CLASSICAL ROOTS OF INTER-UNIVERSAL
TEICHMULLER THEORY ¨
Shinichi Mochizuki (RIMS, Kyoto University)
November 2020

§1. Isogeny invariance of heights of elliptic curves
§2. Crystals and Hodge filtrations
§3. Complex Teichm¨uller theory
§4. Theta function on the upper half-plane

P2
Overview
Analogy with ´etale cohomology, Weil conjectures
←→ classical singular (co)homology of topological spaces
・ Isogeny invariance of heights of elliptic curves (Faltings, 1983)
・ Crystals and Hodge filtrations (Grothendieck, late 1960’s)
・ Complex Teichm¨uller theory (Teichm¨uller, 1930’s)
・ Theta function on the upper half-plane (Jacobi, 19-th century)

P3
§1. Isogeny invariance of heights of elliptic curves
(cf. [Alien], §2.3, §2.4)
We consider elliptic curves.

P21
§4. Theta function on the upper half-plane
(cf. final portion of [Pano], §3; discussion surrounding [Pano], Fig. 4.2)
Recall the theta function on H ∋ z = x + iy, where q def= e^2πiz:
θ(q) def=馬=-∞〜+∞ q^1/2n^2.
Restricting to the imaginary axis (i.e., x = 0) yields, for t def= y:
θ(t) def=馬=-∞〜+∞ e^-πn^2t.
Then the Jacobi identity holds:
θ(t) = t^- 1/2 ・ θ(t^-1).
(引用終り)
以上