We investigate the behavior of standard bases (in the sense of Hironaka and Grauert) for ideals in rings of formal power series over commutative rings with respect to specializations of the coefficients. For instance, we show that any ideal I of the ring of formal power series A[[X]] = A[[X1, . . . , XN ]] with coefficients in a Noetherian ring A admits a standard basis whose image under every ...

Motivated in part by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered λ-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this set has a canonical topology compatible with the filtration on the given filtered ring. For power series rings R[[x]], where R is between Z an...