For every prime p > 0, every n > 0 and \kappa = O(logn), we show the existence of an unsatisfiable system of polynomial equations over O(n log n) variables of degree O(log n) such that any Polynomial Calculus refutation over F_p with M extension variables, each depending on at most \kappa original variables requires size exp(\Omega(n2/(\kappa^2*2^\kappa(M+nlog(n))))) .

Fixed the abstract

For every prime p > 0, every n > 0 and ? = O(logn), we show the existence
of an unsatisfiable system of polynomial equations over O(n log n) variables of degree O(log n) such that any Polynomial Calculus refutation over F_p with M extension variables, each depending on at most ? original variables requires size exp(?????(n2/(?^2*2^?*(M + ????nlog(n))))) .