Tate classes on a product of two Picard modular surfaces

✍ Scribed by Andrew H Knightly

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 222 KB
• Volume: 107
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.04.004

✦ Synopsis

We compute the space of codimension 2 Tate classes on a product of two Picard modular surfaces in terms of automorphic representations on GLðnÞ; no4: The relevant part of the fourth cohomology splits into subspaces indexed by pairs of such automorphic representations. When these representations are not automorphically induced, the corresponding Tate classes are shown to be abelian.