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Results tagged with local-fields
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user 2481
7
votes
0
answers
283
views
Epsilon factors for tamely ramified extensions of local fields
Let $F$ be an unramified extension of $\mathbf{Q}_p$ of degree $n$, and let $K = F(\alpha)$ where $\alpha$ satisfies $\alpha^{p^n - 1} = -p$.
I'm interested in the local $\varepsilon$-factors attache …
- 37k
8
votes
1
answer
520
views
Integral representation of adjoint L-factor for GL(2)
My question is about a local computation in the paper of Gelbart and Jacquet, "A relation between automorphic representations of GL2 and GL3", from 1978.
Let $\sigma$ be an irreducible smooth complex …
- 37k
15
votes
Accepted
Maximal tamely ramified extension of $\mathbf Q_p$
Yes, there is. The maximal unramified extension is obtained by adding all roots of unity of order prime to $p$. The maximal tame extension is obtained by adding on top of that all $n$-th roots of $p$, …
- 37k
29
votes
Accepted
Computing (on a computer) higher ramification groups and/or conductors of representations.
You can also compute some higher ramification groups in Sage. At the moment it gives lower numbering, not upper numbering, but here it is anyway:
sage: Qx.<x> = PolynomialRing(QQ)
sage: g=x^8 + 20*x …
- 37k
9
votes
Reference request for Kato's paper: A generalization of local class field theory by using K ...
I found this old question while searching for Kato's paper myself. Just in case anyone else is also still looking for these, here's what I found.
Kato's work was published in three installments in J. …
- 37k
7
votes
Accepted
A question about mod $p$ local Langlands for $\mathrm{GL}_{2}(\mathbb{Q}_{p})$
You seem to be expecting that mod $p$ local Langlands should satisfy the same compatibilities as "conventional" local Langlands (for smooth representations of $GL_2(\mathbf{Q}_p)$ and $WD(\mathbf{Q}_p …
- 37k