Jim Wright

Hensel's classical lemma – a variant

Related to the Igusa conjectures, Denef and Sperber conjectured a sharp bound for exponential sums mod p^m for general multivariate polynomials with integer coefficients (their local sum conjecture). A key step in verifying this conjecture in two variables is to employ a variant of the classical lemma of Hensel but where the derivative is allowed to degenerate.