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2 votes
1 answer
164 views

What is the sum operation on torsors induced by Weil uniformization?

Let $k$ be an algebraically closed field, $G$ a reductive group, and $C$ a curve. The algebraic version of the Weil uniformization theorem (see e.g. arXiv:1511.06271v2) says that groupoid of $G$-...
Doron Grossman-Naples's user avatar
8 votes
0 answers
469 views

Analog of Ramanujan-Petersson conjecture in Geometric Langlands

The Ramanujan conjecture asserts that \begin{align} |\tau(p)|\leq 2p^{11/2} \end{align} where $\tau(p)$ is the $p^{th}$ Fourier coeffecient in the q-expansion of the weight 12 cusp form $\Delta(z)$. ...
shehryar sikander's user avatar
3 votes
1 answer
988 views

Global Langlands function fields

Has V. Lafforgue proved the automorphic-to-Galois direction in the Global Langlands conjectures for general reductive groups over function fields? What is the current status, more generally? Related ...
user avatar
2 votes
1 answer
753 views

Reference on Casselman-Shalika formula for GL(n) and PGL(n)?

I am looking for reference on Casselman-Shalika formula for GL(n) and PGL(n) at finite place p.
7-adic's user avatar
  • 3,804
8 votes
1 answer
2k views

Why is the Arthur trace formula so powerful?

Considering the Arthur trace formula, why are the sort of convolution operators, whose "normalized traces" are given in geometric terms and spectral terms, actually able to distinguish all ...
Marc Palm's user avatar
  • 11.2k
9 votes
3 answers
1k views

Why is the simple trace formula a weaker tool than the Arthur trace formula?

What are some concrete examples of theorems which can be deduced from the Arthur trace formula, which do not follow from the simple trace of Kazdhan and Flicker? (So I do not mean weaker in the sense ...
Marc Palm's user avatar
  • 11.2k