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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 …
David Loeffler's user avatar
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 $p$, …
David Loeffler's user avatar
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. …
David Loeffler's user avatar
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 …
David Loeffler's user avatar
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 …
David Loeffler's user avatar
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 …
David Loeffler's user avatar