作者：Shlapentokh, A
摘要：Let K be a number field. Let W be a set of non-archimedean primes of K, let O-K,O-W = (x is an element of K \ ord(p)x greater than or equal to 0 For All p is an element of W). Then if K is a totally real non-trivial cyclic extension of Q, there exists an infinite set W of finite primes of K such that Z and the ring of algebraic integers of K have a Diophantine definition over O-K,O-W (Thus, the Diophantine problem of O-K,O-W is undecidable.).
作者：Bierstone, E; Milman, PD
摘要：This article contains an elementary constructive proof of resolution of singularities in characteristic zero, Our proof al,plies in particular to schemes of finite type and to analytic spaces (so we recover the great theorems of Hironaka), We introduce a discrete local invariant inv(X)(a) whose maximum locus determines a smooth centre of blowing up, leading to desingularization, To define inv(X), we need only to work with a category of local-ringed spaces X = (/X/, C-X) satisfying certain natu...
作者：Krstic, S; McCool, J
作者单位：Tufts University; University of Toronto
作者：Tarasov, V; Varchenko, A
作者单位：University of North Carolina; University of North Carolina Chapel Hill
作者：Floyd, W; Parry, W
作者单位：Eastern Michigan University
