$p$-adic functoriality for inner forms of unitary groups in three variables

Ludwig, Judith

doi:10.4310/mrl.2014.v21.n1.a12

Cited by 6 publications

(7 citation statements)

References 9 publications

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“…Other results have been established e.g. in [14], [22] and [26] and by the author in [19]. To our knowledge all known p-adic transfers have in common that classically the transfer works on the level of representations rather than packets, i.e.…”

Section: Introductionmentioning

confidence: 90%

“…This follows from the construction (see Section 3.9 of [18]). For further details the reader may consult Section 3.2.1 of [20].…”

Section: Classical Pointsmentioning

confidence: 99%

“…To our knowledge all known p-adic transfers have in common that classically the transfer works on the level of representations rather than packets, i.e. either one works with groups where stable conjugacy and conjugacy agree or if not one imposes extra conditions (like in [19] a stability condition) to enforce this. In the present work there is no such restriction.…”

Section: Introductionmentioning

confidence: 99%

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A p-adic Labesse–Langlands transfer

Ludwig

2017

manuscripta math.

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Abstract. We prove a p-adic Labesse-Langlands transfer from the group of units in a definite quaternion algebra to its subgroup of norm one elements. More precisely, given an eigenvariety for the first group, we show that there exists an eigenvariety for the second group and a morphism between them that extends the classical Langlands transfer. In order to find a suitable target eigenvariety for the transfer we formalise a notion of Langlands compatibility of tame levels. Proving the existence of Langlands compatible tame levels is the key to pass from the classical transfer on the level of L-packets to a map between classical points of eigenvarieties, which is then amenable for interpolation to give the p-adic transfer.

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Section: Introductionmentioning

confidence: 90%

“…This follows from the construction (see Section 3.9 of [18]). For further details the reader may consult Section 3.2.1 of [20].…”

Section: Classical Pointsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A p-adic Labesse–Langlands transfer

Ludwig

2017

manuscripta math.

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“…This result is an instance of what is now called p-adic Langlands functoriality. Other examples of this can be found in work of Hansen [16], Ludwig [22], and Newton [23].…”

Section: Introductionmentioning

confidence: 91%

The Jacquet–Langlands correspondence for overconvergent Hilbert modular forms

Birkbeck

2019

Int. J. Number Theory

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We use results by Chenevier to interpolate the classical Jacquet-Langlands correspondence for Hilbert modular forms, which gives us an extension of Chenevier's results to totally real fields. From this we obtain an isomorphisms between eigenvarieties attached Hilbert modular forms and those attached to modular forms on a totally definite quaternion algebra over a totally real field of even degree. a In general Chenevier proves that one gets a isomorphism onto the d-new 'part' of the eigenvariety.

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“…Borrowing the terminology of [Lud14, §4.3], we say that and are compatible levels for the symmetric cube transfer for all .…”

Section: The Symmetric Cube Morphisms Of Hecke Algebrasmentioning

confidence: 99%

Galois level and congruence ideal for -adic families of finite slope Siegel modular forms

Conti¹

2019

Compositio Math.

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We consider families of Siegel eigenforms of genus 2 and finite slope, defined as local pieces of an eigenvariety and equipped with a suitable integral structure. Under some assumptions on the residual image, we show that the image of the Galois representation associated with a family is big, in the sense that a Lie algebra attached to it contains a congruence subalgebra of non-zero level. We call Galois level of the family the largest such level. We show that it is trivial when the residual representation has full image. When the residual representation is a symmetric cube, the zero locus defined by the Galois level of the family admits an automorphic description: it is the locus of points that arise from overconvergent eigenforms for GL 2 , via a p-adic Langlands lift attached to the symmetric cube representation. Our proof goes via the comparison of the Galois level with a "fortuitous" congruence ideal, that describes the zero-and one-dimensional subvarieties of symmetric cube type appearing in the family. We show that some of the p-adic lifts are interpolated by a morphism of rigid analytic spaces from an eigencurve for GL 2 to an eigenvariety for GSp 4 . The remaining lifts appear as isolated points on the eigenvariety. at the Laboratoire Analyse, Géométrie et Applications of Université Paris 13.

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$p$-adic functoriality for inner forms of unitary groups in three variables

Abstract: We prove p-adic functoriality for inner forms of unitary groups in three variables by establishing the existence of morphisms between eigenvarieties that extend the classical Langlands functoriality.

Cited by 6 publications

References 9 publications

A p-adic Labesse–Langlands transfer

A p-adic Labesse–Langlands transfer

The Jacquet–Langlands correspondence for overconvergent Hilbert modular forms

Galois level and congruence ideal for -adic families of finite slope Siegel modular forms

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