A relation between standard conjectures and their arithmetic analogues

Details A relation between standard conjectures and their arithmetic analogues A relation between standard conjectures and their arithmetic analogues

1996-08-02

arxiv.org/abs/alg-geom/9608003v1

Mathematics

Algebraic Geometry

AMS-LaTeX file, 10 pages

Scientific paper

In this paper we resolve the arithmetic analogues of standard conjectures for an arithmetic variety, which are proposed by Gillet and Soule, into original standard conjectures and similar conjectures for two cycle class groups. One is the homologically trivial cycles. This is well-known as conjectures about the height pairing raised by Beilinson. The other is the cycle class groups consisting of vertical cycles. We show that the conjectures for the above two cycle class groups with Grothendieck's standard conjectures imply their arithmetic analogues.

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