### 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

### Cite this

*Journal of Number Theory*,

*128*(8), 2492-2504. https://doi.org/10.1016/j.jnt.2008.02.001

}

*Journal of Number Theory*, vol. 128, no. 8, pp. 2492-2504. https://doi.org/10.1016/j.jnt.2008.02.001

**Moduli problem and points on some twisted Shimura varieties of PEL type.** / Virdol, Cristian.

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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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 -