All Questions

Why do we ask Shimura datum to have Hodge weight $(-1,1),(0,0),(1,-1)$? I know it's related to the decomposition of a complex Lie algebra $\frak{g}_{\mathbb{C}}=\frak{t}\oplus\frak{p}^{+} \oplus \frak ...

It's common in subjects that have some version of the "yoga of weights" that you have a functor called "Tate twist" and that the most natural version of it seems like it should be ...