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Results tagged with langlands-conjectures
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user 56878
Higher reciprocity laws
25
votes
Why to believe the Fargues geometrization conjecture?
These notes, from a course Fargues taught at Chicago and transcribed by Sean Howe, are very nice and make a very strong effort to motivate this conjecture and the surrounding theory by analogy with 'h …
- 3,058
8
votes
Accepted
Understanding moduli of shtukas of non-minuscule cocharacter
Yes, in general you need to consider all cocharacters.
$\mathrm{GL}_n$ has the special property that the dominant coweights are all sums of minuscule cocharacters, i.e. ones of the form $[1,\cdots,1 …
- 3,058
28
votes
1
answer
2k
views
Is there a "Langlands philosophy" reason for the fact that the L-function of the Jacobi thet...
The Jacobi theta function $\theta(z) = 1 + 2 \sum_{n = 1}^\infty q^{n^2}$, with $q = e^{\pi i z}$ is a (twisted) modular form with weight $1/2$. It has an associated $L$-function $L(\theta, s) = \sum_ …
- 3,058