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Skippable background: A Whittaker function is more or less a function on a flag manifold which is twisted-invariant for the action of a unipotent subgroup. E.g. consider functions $f$ on $\mathbf{P}^1$...

The idea of proving something by deforming the general case to some special cases is very powerful. For example, one can prove certain equalities by regarding both sides as functions/sheaves, and show ...

After years of putting it off, I finally sat down, read, and understood the classification of connected reductive groups via root data. That's a non-trivial theory! I'm hoping that now that I am done ...

Let $C/K$ be a curve of genus > 2 over a number field $K$ and suppose there exists a $p \in C(K)$. Then a recurring theme in studying $C(K)$ is using the map $C \to J(C)$ normalized by sending $p$ to ...

I am always fascinated when a quadratic form (or a quadric) arises naturally. I have some elementary examples, but most of all, I want to learn more examples. I hope this question isn't considered too ...

The analogy between $O_K$ ($K$ a number field) and affine curves over a field has been very fruitful. It also knows many variations: the field over which the curve is defined may have positive or zero ...