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・4部のIUT論文の簡単なまとめについて

「The rest of part I is largely about the definition of the so-called Hodge
theaters, and some proofs are a bit longer. The category of Hodge theaters has an
extremely complicated definition, but the content of these nontrivial proofs is that their
category is equivalent to the category with one object and automorphism Z/2Z、
and in fact is canonically equivalent to the category of elliptic curves over F isomorphic
to the given E(we note that the functors in both directions are even constructive).
In other words, any Hodge theater comes in a unique way from an elliptic curve
isomorphic to E
. Thus, when the author later chooses an infinite collection of such Hodge theaters,
he might as well choose an infinite collection of elliptic curves isomorphic to E」