  We reduce Hochster's Canonical Element Conjecture (theorem since 2016) to a
localization problem in a characteristic free way. We prove the validity of a
new variant of the Canonical Element Theorem (CET) and explain how a
characteristic free deduction of the new variant from the original CET would
provide us with a characteristic free proof of the CET. We also show that the
Balanced Big Cohen-Macaulay Module Theorem can be settled by a characteristic
free proof if the big Cohen-Macaulayness of Hochster's modification module can
be deduced from the existence of a maximal Cohen-Macaulay complex in a
characteristic-free way.
