Galois representations and torsion cohomology: a series of misunderstandings

Abstract: In 2013, Peter Scholze announced his proof that Galois representations with finite coefficients could be associated to torsion classes in the cohomology of certain locally symmetric spaces. The existence of such a correspondence had been predicted by a number of mathematicians but for a long time no one had the slightest idea how to construct the Galois representations. In this talk I will review some of the history of the problem, with emphasis on the many false starts and occasional successes, and on my own intermittent involvement with this and related problems.

number theory

Audience: researchers in the discipline

( slides | video )

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CHAT (Career, History And Thoughts) series

Series comments: The CHAT series invite established professors to talk about either (1) their math career in general (2) their theorems or theories, but explained from a personal and historical perspective, like how they came up with the problem, what the Aha! moment was like, how the problem changes from its initial form to the published rigorous form.

The idea is that instead of talking about their latest theorems, the speakers would take a step back and talk about the trajectory of an idea, the path to the discovery of a theorem, the influence of ideas learned through a paper or a chance conversation with a colleague, and the hazards met and overcome along the way.

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