| The arithmetic of zero cycles on surfaces with geometric genus and irregularity zero (1991) | |||||||||||||
Abstract | |||||||||||||
| Math Ann Springer Verlag Jim The arithmetic zero cycles surfaces with geometric genus and irregularity zero Kevin Coombes Department Mathematics University Michigan Ann Arbor USA ReceivedMay Introduction Let smooth projective geometrically irreducible surface over perfect field Throughout this paper will assumed that the geometric genus and the irregularity both vanish Denote the separable closure F Let the surface obtained from base extension will also assumed that the group rational equivalence classes zero cycles degree zero vanishes This technical hypothesis which could presumably eliminated the expense working with Ker X For want better name and for ease stating various results any surface which satisfies these three hypotheses will called pseudo rationalsurface Bloch has conjectured that the vanishing should follow from the assumption that This was proven Bloch Kas and Lieberman for all such surfaces which are not general type which have Kodaira dimension less than has also been proven for particular surfaces general type Inose and Mizukami Barlow and Keum Consequently the class pseudo rational surfaces includes rational surfaces Enriques surfaces elliptic surfaces with the classical Godeaux surface Burniat Inoue surfaces Campedelti surfaces and the surfaces Barlow and Keum This paper will study for pseudo rational surfaces defined over fields number theoretic interest Bloch introduced theoretic techniques into the study zero cycles rational surfaces His work was extend. http://deepblue.lib.umich.edu/bitstream/2027.42/46238/1/208_2005_Article_BF01445218.pdf | |||||||||||||
Publication details | |||||||||||||
| |||||||||||||
Cited publications (2) | |||||||||||||
| |||||||||||||