  Thanks to recent results on ring homomorphisms of Azumaya algebras and to the
following ones about endomorphisms of canonical Poisson algebras and Dirac
quantum algebras, and about the reformulation in positive characteristic of
these conjectures in characteristic zero, we prove the equivalence of these
three conjectures in any characteristic, giving also by this way a new proof of
the equivalence of the complex version of the two first conjectures recently
proved by Y. Tsuchimoto.
