p-adic étale cohomology of period domains

Colmez, Pierre; Dospinescu, Gabriel; Hauseux, Julien; Nizioł, Wiesława

doi:10.1007/s00208-020-02139-6

Cited by 5 publications

(5 citation statements)

References 49 publications

(109 reference statements)

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“…Remark 10 We expect that Proposition 9 also holds in the case that F is a local function field. More precisely, we expect that the map (6) for l = p is inverse to the one constructed in [3].…”

Section: Proposition 9 Let F Be a P-adic Field For Every Abelian Prof...mentioning

confidence: 99%

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Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations

Gehrmann

2022

Res Math Sci

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Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld’s upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note, we show that the group of invertible functions is the dual of a universal extension of that Steinberg representation. As an application, we show that lifting obstructions of rigid analytic theta cocycles of Hilbert modular forms in the sense of Darmon–Vonk can be computed in terms of $$\mathcal {L}$$ L -invariants of the associated Galois representation. The same argument applies to theta cocycles for definite unitary groups.

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Section: Proposition 9 Let F Be a P-adic Field For Every Abelian Prof...mentioning

confidence: 99%

“…[21]) and Colmez-Dospinescu-Hauseux-Nizioł (cf. [3]) imply that the extension attached to the identity id : F × → F × can be regarded as a universal extension (see Proposition 9).…”

Section: Introductionmentioning

confidence: 99%

Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations

Gehrmann

2022

Res Math Sci

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“…For R algebraically closed, the conjecture has been proved for the level 0 37 representations of any G or when G has rank 1 (Martin Weissman [201]), G is an inner form of GL(n, F ) (Minguez-Sécherre [138]), or of SL(n, F ) (Peyi Cui [36], [37]), G is a classical group and p = 2 (Shaun Stevens [185], Stevens-Kurinczuk-Daniel Skodlerak [131]) or a quaternionic form of G (Skodlerak [179]), G splits on a moderately ramified extension of F and p does not divide the order of the absolute Weyl group (Jessica Fintzen [66]), Algebraically closed is not necessary and there is an explicit list X of pairs (K, W ) of G where K is an open subgroup of G compact modulo the center and 34 supposing that a uniformizer of F acts trivially 35 ρP is half the sum of the roots of AM in LieP . The formula can be simplified !…”

Section: Representations In Characteristic Different From Pmentioning

confidence: 99%

Representations of $p$-adic groups over coefficient rings

Vignéras¹

2022

Preprint

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Motivated by the Langlands program in representation theory, number theory and geometry, the theory of representations of a reductive p-adic group over a coefficient ring different from the field of complex numbers has been widely developped during the last two decades. This article provides a survey of basic results obtained in the 21st century.7 a global field is a finite extension of Q or of Fp(T ) 8 for F of characteristic p Wee-Teck Gan, Luis Lomeli [70], for F of characteristic 0, Shahidi (A proof of

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“…We expect that Proposition 9 also holds in the case that F is a local function field. More precisely, we expect that the map (5) for l = p is inverse to the one constructed in [CDHN20].…”

Section: Extensions Of Generalized Steinberg Representationsmentioning

confidence: 99%

“…[Orl05]) and Colmez-Dospinescu-Hauseux-Nizio l (cf. [CDHN20]) imply that the extension attached to the identity id : F × → F × can be regarded as a universal extension (see Proposition 9).…”

mentioning

confidence: 99%

Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations

Gehrmann¹

2020

Preprint

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Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld's upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note we show that the group of invertible functions is the dual of a universal extension of that Steinberg representation. As an application, we show that lifting obstructions of rigid analytic theta cocycles of Hilbert modular forms in the sense of Darmon-Vonk can be computed in terms of L-invariants of the associated Galois representation. The same argument applies to theta cocycles for definite unitary groups.

show abstract

p-adic étale cohomology of period domains

Cited by 5 publications

References 49 publications

Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations

Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations

Representations of $p$-adic groups over coefficient rings

Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations

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