Tag Archives: torsion

Ventotene, Part II

I promised to return to a more mathematical summary of the conference in Ventotene, and indeed I shall do so in the next two posts. One of the themes of the conference was bounding the order of the torsion subgroup … Continue reading

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Horizontal Vanishing Conjectures.

Let be a number field, and let be a reductive group over , and let be a congruence subgroup of . I can hear BC objecting that this doesn’t make sense without extra choices; if you have such an objection, … Continue reading

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I don’t know how to prove Serre’s conjecture.

I find it slightly annoying that I don’t know how to prove Serre’s conjecture for imaginary quadratic fields. In particular, I don’t even see any particularly good strategy for showing that a surjective Galois representation — say finite flat with … Continue reading

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Local representations occurring in cohomology

Michael Harris was in town for a few days, and we chatted about the relationship between my conjectures on completed cohomology groups with Emerton and the recent work of Scholze. The brief summary is that Scholze’s results are not naively … Continue reading

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Scholze on Torsion, Part IV

This is a continuation of Part I, Part II, and Part III. I was planning to start talking about Chapter IV, instead, this will be a very soft introduction to a few lines on page 72. At this point, we … Continue reading

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Scholze on Torsion, Part III

This is a continuation of Part I and Part II. Before I continue along to section V.3, I want to discuss an approach to the problem of constructing Galois representations from the pre-Scholze days. Let’s continue with the same notation … Continue reading

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Scholze on Torsion, Part II

This is a sequel to Part I. Section V.1: Today we will talk about Chapter V. We will start with Theorem V.1.4. This is basically a summary of the construction of Galois representations in the RACSDC case, which follows, for … Continue reading

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