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arXiv · 0801.3166

Polygones de Hodge, de Newton et de l'inertie modérée des représentations semi-stables

Xavier Caruso·David Savitt
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Abstract

Let k be a perfect field, and K be a totally ramified extension of K_0 = Frac W(k) of degree e. To a semi-stable p-adic representation of G_K (the absolute Galois group of K), one can classicaly associate two polygons : the Hodge polygon et the Newton polygon. It is well known that the former lies below the latter, and that they have same endpoints. In this note, we introduce a third polygon gotten from the semi-simplification of the representation mod p, and, under some conditions on Hodge-Tate weights, we prove that it lies above the Hodge polygon again with same endpoint. We finally examine one exemple associated to a crystalline representation.

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Xavier Caruso, David Savitt. 2008-06-13. Polygones de Hodge, de Newton et de l'inertie modérée des représentations semi-stables. https://arxiv.org/abs/0801.3166

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