Moduli problem and points on some twisted Shimura varieties of PEL type

Cristian Virdol

Research output: Contribution to journalArticle

Abstract

In this article we describe the moduli problem of a "twist" of some simple Shimura varieties of PEL type that appear in Kottwitz's papers [R. Kottwitz, Shimura varieties and λ-adic representations, in: Automorphic Forms, Shimura Varieties and L-Functions, part 1, in: Perspect. Math., vol. 10, Academic Press, San Diego, CA, 1990, pp. 161-209; R. Kottwitz, Points on some Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (2) (1992) 373-444] and [R. Kottwitz, On the λ-adic representations associated to some simple Shimura varieties, Invent. Math. 108 (1992) 653-665] and then, using the moduli problem, we compute the cardinality of the set of points over finite fields of the twisted Shimura varieties. Using this result, we compute the zeta function of the twisted varieties. The twist of the Shimura varieties is done by a mod q representation of the absolute Galois group of the reflex field of the Shimura varieties.

Original languageEnglish
Pages (from-to)2492-2504
Number of pages13
JournalJournal of Number Theory
Volume128
Issue number8
DOIs
Publication statusPublished - 2008 Aug 1

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Shimura Varieties
Modulus
Twist
Galois field
Automorphic Forms
Galois group
L-function
Riemann zeta function
Set of points
Cardinality

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Virdol, Cristian. / Moduli problem and points on some twisted Shimura varieties of PEL type. In: Journal of Number Theory. 2008 ; Vol. 128, No. 8. pp. 2492-2504.
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Moduli problem and points on some twisted Shimura varieties of PEL type. / Virdol, Cristian.

In: Journal of Number Theory, Vol. 128, No. 8, 01.08.2008, p. 2492-2504.

Research output: Contribution to journalArticle

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