bio | website | math.uchicago.edu/~emerton |
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location | ||
age | 43 | |
visits | member for | 5 years, 8 months |
seen | Jun 25 '14 at 18:53 | |
stats | profile views | 27,737 |
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awarded | Nice Answer |
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awarded | Good Answer |
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awarded | Nice Answer |
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awarded | Enlightened |
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awarded | Nice Answer |
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awarded | Necromancer |
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awarded | Yearling |
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awarded | Nice Answer |
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awarded | Good Answer |
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awarded | Enlightened |
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awarded | Nice Answer |
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awarded | Notable Question |
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awarded | Populist |
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awarded | Nice Answer |
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awarded | Good Answer |
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comment |
When are dual modules free?
@GrahamLeuschke: Dear Graham, I think that the first half is okay provided that $M$ is assumed a priori to have finite projective dimension. (One can proceed by induction on the projective dimension.) Regards, |
Apr
30 |
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Current Status on Langlands Program
@plusepsilon.de: Dear plusepsilon.de, Yes, that's right. But to actually construct/study Galois reps. attached to $GL(n)$ automorphic form, you have to work with unitary groups, for which stable conjugacy and conjugacy are distinct. For example, the proof of Sato--Tate is prima facie about proving cases of symmetric power functoriality from $GL(2)$ to $GL(n)$, and so one could imagine that it doesn't involve stabilization or the fundamental lemma. But in fact, the proof for elliptic curves with integral $j$-invariant depended on the fundamental lemma for unitary groups. Regards, |
Apr
30 |
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Explicit calculation of Weil Deligne representations
Dear Hiro, The case of a Tate curve is particularly easy. The $\ell$-adic Tate module is the Kummer extension of $\mathbb Q_{\ell}$ by $\mathbb Q_{\ell}(1)$ corresponding to the Tate parameter $q$ defining the curve. (This follows directly from the description of the points as $\overline{\mathbb Q}_p^{\times}/q^{\mathbb Z}$.) Now just apply the standard recipe to get the Weil--Deligne representation. Regards, |
Apr
30 |
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Current Status on Langlands Program
Dear Joel, This is an impressive summary of the current status! Cheers, |
Apr
30 |
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Current Status on Langlands Program
@plusepsilon.de: Dear plusepsilon.de, Since many results for $GL(n)$ are proved via transfer to unitary groups, stabilization is in fact an issue, even in the theory for $GL(n)$. Regards, |