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Some thought of p-divisible groups and p-adic Hodge theory

Published at 2024-09-30 22:44:09Viewed 56 times

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Algebraic geometry

Arithmetic geometry

The name "p-divisible group" is somewhat misleading, which in fact has another name "Barsotti-Tate group". A p-divisible group is not merely just a kind of group. lt is more general. In fact, a p-divisible group can be viewed as a tower of affine group schemes with some extra conditions. Historically, p-divisible groups were the main stimulus for p-adic Hodge theory. So l think that studying p-divisible groups is the key to study p-adic Hodge theory.

However, today's p-adic Hodge theory is much more complicated. l failed to understand Fontaine rings in the past. But this won't suppress my interest in p-adic Hodge theory. For now, I'm still studying Peter Scholze's Perfectoid Space, which was published nearly ten years ago and has already obtained a lot of beautiful results. lf l have time, l will still try to study p-adic Hodge theory.

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This short articles was originally published at June 24, 2021.

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