ИСТИНА

Reduction modulo a prime makes the algebra of differential operators finite-dimensional over the center. The center has the structure of a Poisson algebra. Reduction modulo an infinite prime makes it possible to construct a homomorphism between the automorphism group of the Weil angebram on the one hand, and the group of polynomial symplectomorphisms, on the other. We discuss the uniqueness of this homomorphism, i.e. its independence of the choice of an infinitely large prime. We prove that if this homomorphism is isomorphism then it is independent of the choice of an infinitely large prime. We also prove the equivalence between Jacobian and Dixmier conjectures via infinitely large primes.