Advice for p-adic Hodge theory I’m a first year grad…
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Advice for p-adic Hodge theory
I’m a first year grad student trying to learn some p-adic Hodge theory. I am having trouble understanding the motivation behind the formalism of period rings like B\_{dR} or B\_{cris}, and how to think about B-admissible representations. Some people have told me that it’s more important to know how to work with these rather than knowing the motivation, so if anyone can provide some insights on both of these aspects I’d be grateful!
The reason I am learning p-adic Hodge theory is because I keep encountering crystalline representations and the universal deformation rings in the context of R = T theorems, and I just want to know why this is the right notion to study. My advisor has told me that I should take a look at Tate’s “p-divisible groups” since it is one of the first papers in p-adic Hodge theory, so I’m going through it right now and it’s very readable. It’d be great if I can get other references like this as well.
Finally, bonus points if you can give me some rough idea of how the Fargues-Fontaine curve is used for proving things like de Rham implies potentially semistable. Cheers :)
#science
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I’m a first year grad student trying to learn some p-adic Hodge theory. I am having trouble understanding the motivation behind the formalism of period rings like B\_{dR} or B\_{cris}, and how to think about B-admissible representations. Some people have told me that it’s more important to know how to work with these rather than knowing the motivation, so if anyone can provide some insights on both of these aspects I’d be grateful!
The reason I am learning p-adic Hodge theory is because I keep encountering crystalline representations and the universal deformation rings in the context of R = T theorems, and I just want to know why this is the right notion to study. My advisor has told me that I should take a look at Tate’s “p-divisible groups” since it is one of the first papers in p-adic Hodge theory, so I’m going through it right now and it’s very readable. It’d be great if I can get other references like this as well.
Finally, bonus points if you can give me some rough idea of how the Fargues-Fontaine curve is used for proving things like de Rham implies potentially semistable. Cheers :)
#science
source
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