# What is Drinfeld's manuscript “Best Dream” (in Russian!) about?

I would like to know what Drinfeld's scanned manuscript "Best Dream" is about: the title makes me curious.

It's in Russian.

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From the first line it appears to about D-modules on stacks.

The next topic is an attempt to construct a "duality" (called F) for derived category of (quasicoherent) D-modules on Bun_G (the space/stack of G-bundles). The problem is to find a "reverse Langlands transform" (?) by defining a suitable scalar product on those.

In the middle a single question appears, "What is the Eisenstein fuctor?" (indeed, what is it?) Next, there's a question about Hecke functors.

Part two starts with the self-explanatory

        D (Bun_G)  =?=  O(LocSys)


The Eisenstein functor for GL(2) appears in the discussion, with the standard definition. Some constructions relevant to the formula above appear. Pages 59–60 then are in English. Then the derived categories and Eisentein functor continue.

Page 76 contains some specific questions ("I don't understand!") again along the topics above which continue until the end of paper.

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Many thanks! I'd be happy about any more explanations. –  Thomas Riepe Oct 25 '09 at 20:36
I kind of started posting questions about it with mathoverflow.net/questions/2515/what-is-eisenstein-series –  Ilya Nikokoshev Oct 25 '09 at 21:27