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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

21 votes
1 answer
4k views

What is the current status of the function fields Langlands conjectures?

My question, roughly speaking is, what happened to the function fields Langlands conjecture? I understand around 2000 (or slightly earlier perhaps), Lafforgue proved the function fields Langlands corr …
Puraṭci Vinnani's user avatar
5 votes

Number Theory and Geometry/Several Complex Variables

"Higher dimensional geometry" traditionally doesn't mean this I think, so this is only partially relevant to your question (and this isn't really related to complex analysis side); if you broaden your …
Puraṭci Vinnani's user avatar
1 vote

cohomology of moduli spaces

This is for Shimura varieties only; I've read only parts of the introduction so I don't know exactly what's done, but both seem to be related to $l$-adic cohomology of Shimura varieties : Taylor & …
Puraṭci Vinnani's user avatar