Some special cases of Chow groups of complete ramified regular local rings

Abstract

In this thesis we study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, (I) = 0 in $A\sb{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, (P) = 0 in $A\sb{n-i}(R).$ We also study the above problem when the Eisenstein polynomial is of the form $f = p + X\sbsp{1}{t\sb1} + X\sbsp{2}{t\sb2} + X\sbsp{3}{t\sb3} + X\sbsp{4}{2} + X\sbsp{5}{2}$ and $f = p + X\sbsp{1}{2} + \cdots + X\sbsp{n-2}{2} + X\sbsp{n-1}{4} + X\sbsp{n}{4}.$ Several other cases of the problem are also established.