 The Picard Variety of an Arbitrary VarietySerge Lang
Chapter Chapter VI in Abelian Varieties, 1983, pp 147-177 from Springer Abstract: Abstract We are going to see in this chapter how one can prove the existence of the Picard variety of a variety V, complete and non-singular in codimension 1 in a simple manner, once one knows the existence of the Picard variety of an abelian variety. The Picard variety of V is derived functiorially from that of its Albanese variety, and we shall use this fact to get the theory of divisiorial correspondences on a product U x V. As a special case, we obtain the theory of correspondences on a curves, which gives us the Lefschetz fixed point formula. The group of cor- respondence classes of the curve is isomorphic to the group of an endomorphism corresponds to the characteristic polynomial of the representation of the endomorphism on the first homology group (in the classical case), and its trace is the trace of this representation. Combining the Lefschetz fixed point formula with the results of Chapter V, we obtain in a natural way the Riemann hypothesis for curves. Keywords: Inverse Image; Abelian Variety; Riemann Hypothesis; Generic Translation; Picard Group (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-8534-7_6 Ordering information: This item can be ordered from DOI: 10.1007/978-1-4419-8534-7_6 Access Statistics for this chapter More chapters in Springer Books from Springer |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.