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arXiv · 2303.05472

Tangent spaces on the trianguline variety at companion points

Seginus Mowlavi
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Abstract

Many results about the geometry of the trianguline variety have been obtained by Breuil-Hellmann-Schraen. Among them, using geometric methods, they have computed a formula for the dimension of the tangent space of the trianguline variety at dominant crystalline generic points, which has a conjectural generalisation to companion (i.e. non-dominant) points. In an earlier work, they proved a weaker form of this formula under the assumption of modularity using arithmetic methods. We prove a generalisation of a result of Bella\"iche-Chenevier in p-adic Hodge theory and use it to extend the arithmetic methods of Breuil-Hellmann-Schraen to a wide class of companion points.

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Seginus Mowlavi. 2023-03-09. Tangent spaces on the trianguline variety at companion points. https://arxiv.org/abs/2303.05472

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