What is Drinfeld's manuscript "Best Dream" (in Russian!) about? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T07:00:42Z http://mathoverflow.net/feeds/question/2464 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/2464/what-is-drinfelds-manuscript-best-dream-in-russian-about What is Drinfeld's manuscript "Best Dream" (in Russian!) about? Thomas Riepe 2009-10-25T12:56:44Z 2009-10-25T19:07:00Z <p>I would like to know what Drinfeld's <a href="http://math.uchicago.edu/~drinfeld/bestdream.pdf" rel="nofollow" title="low res, high res on his website">scanned manuscript</a> "Best Dream" is about: the title makes me curious. </p> <p>It's in Russian.</p> http://mathoverflow.net/questions/2464/what-is-drinfelds-manuscript-best-dream-in-russian-about/2498#2498 Answer by Ilya Nikokoshev for What is Drinfeld's manuscript "Best Dream" (in Russian!) about? Ilya Nikokoshev 2009-10-25T18:49:42Z 2009-10-25T19:07:00Z <p>From the first line it appears to about <strong>D-modules on stacks</strong>.</p> <p>The next topic is an attempt to construct a "duality" (called F) for derived category of (quasicoherent) D-modules on <code>Bun_G</code> (the space/stack of G-bundles). The problem is to find a "reverse Langlands transform" (?) by defining a suitable scalar product on those.</p> <p>In the middle a single question appears, "What is the Eisenstein fuctor?" (indeed, what is it?) Next, there's a question about Hecke functors.</p> <p>Part two starts with the self-explanatory</p> <pre><code> D (Bun_G) =?= O(LocSys) </code></pre> <p>The Eisenstein functor for <code>GL(2)</code> appears in the discussion, with the standard definition. Some constructions relevant to the formula above appear. Pages 59&ndash;60 then are in English. Then the derived categories and Eisentein functor continue.</p> <p>Page 76 contains some specific questions ("I don't understand!") again along the topics above which continue until the end of paper.</p>