All Questions
6 questions
5
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Motivic $L$-functions came from automorphic representations
Langlands in his 1978 ICM talk made a conjecture that all motivic $L$-functions should arise as automorphic $L$-functions. A part of this conjecture, namely for some Hasse-Weil $\zeta$ functions is a ...
- 607
6
votes
1
answer
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Relationship between motivic Galois groups and Langlands program [duplicate]
I would like to know if there is any relationship between the motivic Galois groups and the Langlands program.
Many thanks.
- 1,720
15
votes
2
answers
2k
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The status of automorphic induction
Background: Let $K/F$ be a degree $r$ extension of number fields. It is conjectured that an automorphic representation of GL$_n$ associated to $K$ induces an automorphic representation of GL$_{rn}$ ...
- 1,704
5
votes
0
answers
654
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The Shafarevich Conjecture and motivic Langlands stacks.
Hi, I recently learned about an amazing conjecture of Shafarevich
(proved by Faltings) about the finiteness of the number
of curves of a fixed genus with good reduction outside a
finite number of ...
6
votes
1
answer
688
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Followup questions about the relationship between modular forms and motives
It occurs more and more that I ask a question on math stackexchange and then realize that it is more appropriate to mathoverflow. Hopefully this reflects well on myself... In any case, I copy here ...
- 61
10
votes
1
answer
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How does the conjectural Langlands group fit into the Tannakian point of view?
I've read that one way to formulate the Langlands program is the following:
Let $\mathcal{L}_ {\mathbb{Q}}$ be the conjectural Langlands group. Then the category of semi-simple (continuous) ...