A relation between standard conjectures and their arithmetic analogues

1996/08/02 by Yuichiro Takeda, Takeda, Yuichiro
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9608003

AMS-LaTeX file, 10 pages

arxiv created 1996/08/02 · arxiv updated 2009/11/30

Abstract

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.

Related

• Standard Conjectures and Height Pairings
• Hodge index theorem for arithmetic cycles of codimension one
• Higher Arithmetic Intersection Theory
• Building bridges between Tate conjectures and arithmetic invariants
• The Business of Height Pairings