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Results tagged with langlands-conjectures
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user 2623
Higher reciprocity laws
6
votes
3
answers
966
views
examples of admissible representations of $GL_{n}(K)$ over p-adic field
I've been reading about the Langlands program (the paper by Torsten Wedhorn "Local langlands correspondence for GL(n) over p-adic fields, to be precise), and I want to get my hands dirty with examples …
- 2,216
1
vote
1
answer
362
views
From Galois representations to automorphic forms for $\mathfrak{sl}_2$ (via Drinfeld's shtukas)
Drinfeld-Lafforgue have proven function fields Langlands conjectures in type A: see https://arxiv.org/pdf/math/0212417.pdf (Laumon's survey in English), https://arxiv.org/pdf/math/0212399.pdf (LLaffor …
- 2,216
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 …
- 2,216
5
votes
1
answer
887
views
Can Taniyama-Shimura conjecture be generalized to curves of higher genus (within Langlands f...
The Shimura-Taniyama-Weil conjecture asserts that if E is an elliptic curve over Q, then there is an integer N ≥ 1 and a weight-two cusp form f of level N, normalized so that a1(f) = 1, such that ap(E …
- 2,216
7
votes
1
answer
542
views
Examples of function fields Langlands for small genus (<= 2)
See Edward Frenkel's article "Lectures on the Langlands program and conformal field theory" for an exposition of the function fields Langlands correspondence (now a theorem of Drinfel'd, L.Lafforgue & …
- 2,216