Shimura Varieties: motivation

EDIT: While these notes might be still useful to read, if one wants a more in-depth explanation of the ideas below see the notes from this post.

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This will be the first in a series of posts discussing Shimura varieties. In particular, we will focus here on a sort of broad motivation for the subject—why Shimura varieties are a natural thing to study and, in particular, what they give us.

Local class field theory: a discussion

In this post we discuss local class field theory (specifically looking at -adic fields) with a focus on the broader picture, and the multiple approaches.