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I am really interested in reading the work of L.Lafforgue and V.Lafforgue about langlands correspondence in function field case. After some search work, it seems that Cohomology of drinfeld modular Variety by Laumon is a good choice for the basic relevant materials. So is it a right book to read? Or do you have any suggestion?

I have taken courses of algebraic number theory, algebraic geometry, modular form and some automorphic representation. But do not know much about trace formula. Almost nothing about Drinfeld module, shtuka(which I really want to learn)

Thanks!

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It depends a little bit on what you want to learn I guess. To my knowledge V. Lafforgue avoids the use of trace formulas completely. He himself has written a very nice (and quite detailed) introduction to his work, that you can find here: https://arxiv.org/abs/1404.3998 .

Moreover there is a nice introduction to this introduction by Jochen Heinloth: https://www.uni-due.de/~hm0002/Artikel/VortragVIAS2016.pdf

You will find more references in these articles.

Lastly I want to say that I am of course no expert on any of this (for instance I have not really studied the work of Laumon), and there are a lot of people who could give you better advice. These people are possibly not visiting this site however, and you will probably get better answers at mathoverflow (since the material is quite advanced I don't think anyone would complain if you asked this question there).

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