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I have to understand Deligne's paper" Hodge cycles on abelian variesties",but I find it very difficlut to read ,even though I have already spent several months to learn the etale cohomology.Is there any sugestion for understanding this paper,or any auxiliary reading material? Thanks a lot !

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    $\begingroup$ There is a paper of Gross on the Chowla--Selberg formula (from the early 80s, I think) which may have served as partial inspiration for Deligne. It is more accessible, I would guess. Also, have you looked in the Motives volumes? I don't remember if there is anything expository about absolute Hodge cycles there, but you could look. $\endgroup$
    – Emerton
    Mar 9, 2010 at 18:45
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    $\begingroup$ -1, because I just don't like questions like this. I guess a "correct answer" would be like Emerton's comment: a more accessible prequel. But what OP is really asking is for someone to explain that paper here. Asking about individual remarks in the paper seems like a good idea, because it advances the community. But "this paper is hard" isn't much of a question, and is better suited as an impetus to set up a student seminar on the topic than to start a discussion here. In any case, the actual answer is: "read papers you like, and come back to this one later." $\endgroup$ Mar 9, 2010 at 19:09
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    $\begingroup$ I like Schappacher's book Periods of Hecke Characters. It's also available for cheap. $\endgroup$ Mar 9, 2010 at 20:14
  • $\begingroup$ Have you read Deligne's series, Theorie de Hodge? $\endgroup$
    – S. Carnahan
    Mar 10, 2010 at 6:33
  • $\begingroup$ Seconding Theo's comment. A more focused question would be helpful - part of being or becoming a good student is to work out more precisely why/where one is stuck. (I speak as someone who is rather slow at doing this, but it does need to be done.) $\endgroup$
    – Yemon Choi
    Mar 11, 2010 at 11:24

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