Purity for Hodge-Tate representations

Tsuji, Takeshi

doi:10.1007/s00208-010-0582-7

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…It can also be regarded as a relative version of Sen's theory. Our improvement here is that when L is defined over X (rather than X K ), the Higgs field is nilpotent (we learned from Abbes that a similar nilpotence statement already appeared in [Br1, Proposition 5] and [Ts,Lemma 9.5]). Our approach is different from loc.…”

Section: The P-adic Simpson Correspondencementioning

confidence: 85%

Rigidity and a Riemann–Hilbert correspondence for p-adic local systems

2016

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We construct a functor from the category of p-adic étale local systems on a smooth rigid analytic variety X over a p-adic field to the category of vector bundles with an integrable connection on its "base change to B dR ", which can be regarded as a first step towards the sought-after p-adic RiemannHilbert correspondence. As a consequence, we obtain the following rigidity theorem for p-adic local systems on a connected rigid analytic variety: if the stalk of such a local system at one point, regarded as a p-adic Galois representation, is de Rham in the sense of Fontaine, then the stalk at every point is de Rham. Along the way, we also establish some basic properties of the p-adic Simpson correspondence. Finally, we give an application of our results to Shimura varieties. R.

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Section: The P-adic Simpson Correspondencementioning

confidence: 85%

Rigidity and a Riemann–Hilbert correspondence for p-adic local systems

2016

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“…Tsuji obtained Theorem 5.5 in the case of semistable schemes [Tsu11, Theorem 9.1]. He also gave a characterization of Hodge–Tate local systems in terms of restrictions to divisors.…”

Section: Applications and Related Topicsmentioning

confidence: 99%

“…He also gave a characterization of Hodge–Tate local systems in terms of restrictions to divisors. See [Tsu11, Theorem 9.1] for the detail.…”

Section: Applications and Related Topicsmentioning

confidence: 99%

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Constancy of generalized Hodge–Tate weights of a local system

Shimizu¹

2018

Compositio Math.

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Sen attached to each $p$-adic Galois representation of a $p$-adic field a multiset of numbers called generalized Hodge–Tate weights. In this paper, we discuss a rigidity of these numbers in a geometric family. More precisely, we consider a $p$-adic local system on a rigid analytic variety over a $p$-adic field and show that the multiset of generalized Hodge–Tate weights of the local system is constant. The proof uses the $p$-adic Riemann–Hilbert correspondence by Liu and Zhu, a Sen–Fontaine decompletion theory in the relative setting, and the theory of formal connections. We also discuss basic properties of Hodge–Tate sheaves on a rigid analytic variety.

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Crystalline $$\mathbb {Z}_p$$-Representations and $$A_{\inf }$$-Representations with Frobenius

Tsuji

2020

Simons Symposia

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Purity for Hodge-Tate representations

Cited by 5 publications

References 17 publications

Rigidity and a Riemann–Hilbert correspondence for p-adic local systems

Rigidity and a Riemann–Hilbert correspondence for p-adic local systems

Constancy of generalized Hodge–Tate weights of a local system

Crystalline $$\mathbb {Z}_p$$-Representations and $$A_{\inf }$$-Representations with Frobenius

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