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 language | English |
|---|---|
| Pages (from-to) | 2492-2504 |
| Number of pages | 13 |
| Journal | Journal of Number Theory |
| Volume | 128 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 2008 Aug 1 |
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All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
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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 journal › Article
TY - JOUR
T1 - Moduli problem and points on some twisted Shimura varieties of PEL type
AU - Virdol, Cristian
PY - 2008/8/1
Y1 - 2008/8/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=44949229087&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2008.02.001
DO - 10.1016/j.jnt.2008.02.001
M3 - Article
VL - 128
SP - 2492
EP - 2504
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
IS - 8
ER -