Homological vanishing theorems for locally analytic representations

Kohlhaase, Jan; Schraen, Benjamin

doi:10.1007/s00208-011-0680-1

Cited by 7 publications

(12 citation statements)

References 30 publications

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“…Notably the case of GL h (K) acting on Drinfeld's p-adic upper half space was studied in detail and found applications to the de Rham cohomology of p-adically uniformized varieties (cf. [KS12]).…”

Section: Introductionmentioning

confidence: 99%

On the Iwasawa theory of the Lubin–Tate moduli space

Kohlhaase

2013

Compositio Math.

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We study the affine formal algebra R of the Lubin-Tate deformation space as a module over two different rings. One is the completed group ring of the automorphism group Γ of the formal module of the deformation problem, the other one is the spherical Hecke algebra of a general linear group. In the most basic case of height two and ground field Q p , our structure results include a flatness assertion for R over the spherical Hecke algebra and allow us to compute the continuous (co)homology of Γ with coefficients in R. Contents

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Section: Introductionmentioning

confidence: 99%

On the Iwasawa theory of the Lubin–Tate moduli space

Kohlhaase

2013

Compositio Math.

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“…After giving a brief overview on Kohlhaase and Schraen's Koszul resolution of locally analytic principal series (see [KS12]) we recall the control theorem relating overconvergent cohomology to classical cohomology as proven by Ash-Stevens, Urban and Hansen (see [AS08], [Urb11] and [Han17]). Combining the two results allows us to construct classes in the cohomology of (duals of) principal series.…”

Section: Overconvergent Cohomologymentioning

confidence: 99%

“…Under this assumption Kohlhaase and Schraen constructed a Koszul resolution of locally analytic principal series representations (cf. [KS12]), which we recall in Section 3.1. Using that resolution we can lift overconvergent cohomology classes which are common eigenvectors for all U p -operators to big cohomology classes.…”

Section: Introductionmentioning

confidence: 99%

Big principal series, p-adic families and L-invariants

Gehrmann¹,

Rosso²

2020

Preprint

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In earlier work, the first named author generalized the construction of Darmon-style L-invariants to cuspidal automorphic representations of semisimple groups of higher rank, which are cohomological with respect to the trivial coefficient system and Steinberg at a fixed prime.In this paper, assuming that the Archimedean component of the group has discrete series we show that these automorphic L-invariants can be computed in terms of derivatives of Hecke-eigenvalues in p-adic families. Our proof is novel even in the case of modular forms, which was established by Bertolini, Darmon, and Iovita. The main new technical ingredient is the Koszul resolution of locally analytic principal series representations by Kohlhaase and Schraen.As an application of our results we settle a conjecture of Spieß: we show that automorphic L-invariants of Hilbert modular forms of parallel weight 2 are independent of the sign character used to define them. Moreover, we show that they are invariant under Jacquet-Langlands transfer and, in fact, equal to the Fontaine-Mazur L-invariant of the associated Galois representation. Under mild assumptions, we also prove the equality of automorphic and Fontaine-Mazur L-invariants for representations of definite unitary groups of arbitrary rank.Finally, we study the case of Bianchi modular forms to show how our methods, given precise results on eigenvarieties, can also work in the absence of discrete series representations.

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“…An important example was studied by Drinfeld (cf. Kohlhaase and Schraen 2012). The generic fiber of the representing formal scheme is known as Drinfeld's upper half space over K. Instead of continuous representations of Aut.G/ as in Theorem 4, it gives rise to an important class of p-adic locally analytic representations in the sense of Schneider and Teitelbaum.…”

Section: Propositionmentioning

confidence: 99%