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Oct 19, 2017 at 13:27 comment added Will Sawin @wkf I didn't say it gave more representations - although I didn't know / didn't remember that it actually gave less, thanks. What I said is that it gives a geometrically stronger statement, i.e. the representations actually appear in the cohomology of a curve / family of curves.
Oct 19, 2017 at 12:21 comment added wkf I think Drinfeld first proved certain cases of GL_2 (those representations being Steinberg) in his thesis using Drinfeld modules and later proved the full result for GL_2 using shtukas. So I am wondering why you said using Drinfeld modular varieties would give more representations than using moduli stacks of shtukas.
Aug 24, 2017 at 22:06 comment added user40276 Just for completeness. A reference where the relation between shtukas, Anderson T-motives and Drinfeld modules is stablished is the following springer.com/gp/book/9783540635413
Aug 24, 2017 at 16:54 history asked Will Sawin CC BY-SA 3.0