Abstract
In this lecture the main steps in the proof of the Tate conjectures for Hilbert-Blumenthal surfaces will be discussed. This conjecture was proved for most cases by Harder, Langlands and Rapoport in their fundamental paper [9]. The remaining cases are covered by my thesis [11]. Recently Ramakrishnan and Murty gave a different proof for these remaining cases in their paper [14]. For more information on Hilbert-Blumenthal surfaces, especially on the Beilinson conjectures, I recommend the excellent survey article of Ramakrishnan [16]. I would like to thank Professor G. Henniart very much for inviting me to this seminar.
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Klingenberg, C. (1987). Survey of the Proof of the Tate Conjectures for Hilbert-Blumenthal Surfaces. In: Goldstein, C. (eds) Séminaire de Théorie des Nombres, Paris 1985–86. Progress in Mathematics, vol 71. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-4267-1_6
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