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What is a good reference for the story of congruences such as

$$\displaystyle \tau(n) \equiv \sigma(11)(n) \mod\ 691$$

with a conceptual explanation with connections to étale cohomology, etc?

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Brian Conrad was writing a book on this and it was available on his web site. However, the PDF link there seems not to work any more. If it has been published that would be a modern source complementing the Swinnerton-Dyer notes. –  T.. Nov 24 '10 at 17:51
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@T..: Dear T.., I don't believe that Brian's book has been published (so far). –  Matt E Nov 26 '10 at 4:45
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2 Answers

The paper of Swinnerton-Dyer in Lecture Notes in Math 350, as well as Serre's Bourbaki talk on the same topic.

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The paper of Deligne, Formes modulaires et représentations $l$-adiques, available at numdam, has these things.

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