questions on Deligne's letter to Piatetski-Shapiro - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T11:23:23Z http://mathoverflow.net/feeds/question/56620 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/56620/questions-on-delignes-letter-to-piatetski-shapiro questions on Deligne's letter to Piatetski-Shapiro Przemyslaw Chojecki 2011-02-25T10:00:08Z 2011-02-25T10:00:08Z <p>Now, that the letter is to be found here: <a href="http://www.math.ias.edu/~jaredw/DeligneLetterToPiatetskiShapiro.pdf" rel="nofollow">http://www.math.ias.edu/~jaredw/DeligneLetterToPiatetskiShapiro.pdf</a> ,I'd have a couple of questions concerning it. Actually, I have a problem only with the very last page. Could any one explain with more details the reasoning after Deligne proves $$H^0 = \oplus _{\chi} Hom _{H(\mathbb{R}) \times H(\mathbb{Q} _p)} (Sym ^k (V) \otimes ..., L_0)$$</p> <p>1) Is the representation of $H(\mathbb{A} ^f)$ he talks about, the one which comes from the action of $H(\mathbb{A} ^f)$ on $L_0 (...)$ inside the $Hom$? </p> <p>2) Why "the following representation occurs in $\kappa (\mu)$"?</p> <p>3) Why "supercuspidal representations cannot occur outside" $\kappa (\mu)$ and what are references to which Pierre Deligne alludes (especially I am interested in "Langlands + vanishing cycle" method)?</p> <p>4) How he deduces Theorem C from all this?</p> <p>I hope, it is not too much to ask in one post. </p>