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On mod p non-abelian Lubin-Tate theory for GL_2(Q_p)

We analyse the mod p étale cohomology of the Lubin-Tate tower both with compact support and without support. We prove that there are no supersingular representations in the H^1_c of the Lubin-Tate tower. On the other hand, we show that in H^1 of the Lubin-Tate tower appears the mod p local Langlands correspondence and the mod p local Jacquet-Langlands correspondence, which we define in the text. We discuss the local-global compatibility part of the Buzzard-Diamond-Jarvis conjecture which appears naturally in this context.

preprint2013arXivOpen access
Przemyslaw Chojecki
math.AGmath.NT
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Przemyslaw Chojecki

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