Lefschetz Properties of Subvarieties of Shimura Varieties

T. N. Venkataramana

Type: Book-Chapter

Publication Date: 2002-01-01

Citations: 1

DOI: https://doi.org/10.1007/978-93-86279-09-5_24

Abstract

We give examples of cycle classes on certain unitary Shimura varieties which are not generated by Hecke translates of classes of Shimura subvarieties. We also give examples of cohomology classes (of low degree) which do not survive on any Shimura subvariety, thereby showing that the span of Hecke translates of Shimura subvarieties can never contain the class of an ample subvariety.

Locations

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Works Cited by This (10)

Action	Title	Year	Authors
+	Non-vanishing theorems for the cohomology of certain arithmetic quotients.	1992	Jianshu Li
+ PDF Chat	None	2001	T. N. Venkataramana
+	Theta functions and holomorphic differential forms on compact quotients of bounded symmetric domains	1983	Greg W. Anderson
+	Unitary representations with non-zero cohomology	1984	David A. Vogan Gregg J. Zuckerman
+	Restriction of the holomorphic cohomology of a Shimura variety to a smaller Shimura variety	1998	Laurent Clozel T. N. Venkataramana
+	On the cohomology of Kottwitz’s arithmetic varieties	1993	Laurent Clozel
+	Algebraische Zyklen auf Hilbert-Blumenthal-Flächen.	1986	G. Harder R.P. Langlands
+	Die Tate-Vermutungen f�r Hilbert-Blumenthal-Fl�chen	1987	Christoph Klingenberg
+	Period relations and the Tate conjecture for Hilbert modular surfaces	1987	V. Kumar Murty Dinakar Ramakrishnan
+	A lefschetz property for subvarieties of shimura varieties	1998	Michael Harris Jian-Shu Li