Intersection numbers of Hecke cycles on Hilbert modular varieties
Journal Article
Let Script O sign be the ring of integers of a totally real number field E and set G := ResE/ℚ( GL2). Fix an ideal c ⊂ Script O sign. For each ideal m ⊂ Script O sign let T(m) denote the mth Hecke operator associated to the standard compact open subgroup Uo(c) of G(double-struck Af). Setting X0(c) := G(ℚ)\G(double-struck A)/K∞U0(c), where K ∞ is a certain subgroup of G(ℝ), we use T(m) to define a Hecke cycle Z(m) ∈ IH2[E:ℚ](X0(c) x X 0(c)). Here IH• denotes intersection homology. We use Zucker's conjecture (proven by Looijenga and independently by Saper and Stern) to obtain a formula relating the intersection number Z(m)·Z(n) to the trace of *T(m) ○ T(n) considered as an endomorphism of the space of Hilbert cusp forms on U0(c). © 2007 by The Johns Hopkins University Press.
Full Text
Duke Authors
Cited Authors
- Getz, J
Published Date
- December 1, 2007
Published In
Volume / Issue
- 129 / 6
Start / End Page
- 1623 - 1658
International Standard Serial Number (ISSN)
- 0002-9327
Digital Object Identifier (DOI)
- 10.1353/ajm.2007.0041
Citation Source
- Scopus