| This thesis consists of two distinct parts held together by the guiding principle of the interplay between algebraic topology and algebraic geometry. The first part "An Algebraic Napier-Ramachandran Theorem", gives an algebraic proof of a theorem proved by Napier and Ramachandran using the {dollar}Lsp2-bar{lcub}partial{rcub}{dollar} lemma. The main theorem is:; Theorem. Let {dollar}Zto X{dollar} be an unramified map of one smooth, geometrically connected, projective, positive dimensional variety over a field k of finite characteristic to another, and suppose that the normal bundle {dollar}Nsb{lcub}Z/X{rcub}{dollar} is ample. Then the image of the map {dollar}pisbsp{lcub}1{rcub}{lcub}et{rcub}(Z)topisbsp{lcub}1{rcub}{lcub}et{rcub}(X){dollar} has finite index.; The second part is a construction of cohomology operations on Chow groups which commute with Steenrod operations under the cycle class map. It is a direct application of the recent work of D. Edidin and W. Graham on Equivariant Chow Theory. |
