Geodesic
Hodge-Newton filtration for $p$-divisible groups with ramified endomorphism structure
Documenta mathematica, Tome 27 (2022), pp. 1805-1863.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $\mathcal{O}_K$ be a complete discrete valuation ring of mixed characteristic $(0, p)$ with perfect residue field. We prove the existence of the Hodge-Newton filtration for $p$-divisible groups over $\mathcal{O}_K$ with additional endomorphism structure for the ring of integers of a finite, possibly ramified field extension of $\mathbb{Q}_p$. The argument is based on the Harder-Narasimhan theory for finite flat group schemes over $\mathcal{O}_K$. In particular, we describe a sufficient condition for the existence of a filtration of $p$-divisible groups over $\mathcal{O}_K$ associated to a break point of the Harder-Narasimhan polygon.
Classification : 14L05
Keywords: \(p\)-divisible groups, Hodge-Newton filtration, Harder-Narasimhan theory, ramified PEL structure 
@article{DOCMA_2022__27__a20,
     author = {Marrama, Andrea},
     title = {Hodge-Newton filtration for \(p\)-divisible groups with ramified endomorphism structure},
     journal = {Documenta mathematica},
     pages = {1805--1863},
     publisher = {mathdoc},
     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a20/}
}
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Marrama, Andrea. Hodge-Newton filtration for \(p\)-divisible groups with ramified endomorphism structure. Documenta mathematica, Tome 27 (2022), pp. 1805-1863. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a20/