一个由Frobenius平方固定的非平凡束族

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI:10.1016/S0764-4442(01)02109-7

Yves Laszlo

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引用次数: 12

摘要

一个证明了F2上的光滑投影曲线的存在性，以及X⊗k的算术基本群具有SL2(k[[t]])中值的表示的存在性，具有k个特征2的合适有限域，使得几何基本群的像是无限的。这对德容的一个问题给出了否定的回答。

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A non-trivial family of bundles fixed by the square of Frobenius

One shows the existence of a smooth projective curve over $F_{2}$ and of representations of the arithmetic fundamental group of X⊗k with values in $SL_{2} (k[[t]])$ , with k suitable finite field of characteristic 2, such that the image of the geometric fundamental group is infinite. This gives a negative answer to a question of A.J. de Jong.

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Comptes Rendus de l'Académie des Sciences - Series I - Mathematics

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