Abstract not found

Abstract—It is shown that black-box derandomization of polynomial identity testing (PIT) is essentially equivalent to derandomization of Noether’s Normalization Lemma for explicit algebraic varieties, the problem that lies at the heart of the foundational classification problem of algebraic geometry. Specifically: (1) It is shown that in characteristic zero black-box derandomization of the symbolic trace identity testing (STIT) brings the problem of derandomizing Noether’s Normalization Lemma for the ring of invariants of the adjoint action of the general linear group on a tuple of matrices from EXPSPACE (where it is currently) to P. Next it is shown that assuming the Generalized Riemann Hypothesis (GRH), instead of the blackbox derandomization hypothesis, brings the problem from EXPSPACE to quasi-PH, instead of P. Thus black-box derandomization