Could anyone point me to a place where I could find Deligne's letter to Piatetskii-Shapiro from 1973? It is cited for example in Berkovich's "Vanishing cycles for formal schemes II".



Deligne's letter to Piatetskii-Shapiro from 1973
I have typeset Deligne's letter, and placed the result here:


<http://www.math.ias.edu/~jaredw/DeligneLetterToPiatetskiShapiro.pdf>


I have made some minor edits so that the text reads more naturally to a native speaker of English. Also I made a few annotations where I truly believe there is an error in the original. Any other errors are mine.


The letter struck me with how much it accomplishes in such a short space. Actually, I would say that the meat of the argument is confined to the final three pages, with the rest there only to establish notation. This letter ought to be required reading for anyone studying automorphic forms in arithmetic!


