User 750am - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T21:19:21Z http://mathoverflow.net/feeds/user/24003 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/98103/1-dimensional-semi-stable-galois-representations-with-coefficients 1-dimensional semi-stable Galois representations with coefficients 750am 2012-05-27T11:51:20Z 2012-05-27T14:43:23Z <p>For any p-adic local field K, all 1-dim <strong>semi-stable</strong> Galois repn: $G_K \to Q_p^{*}$ are just $Q_p(n)\otimes \mu$, where $Q_p(n)$ is the Tate twist of cyclotomic character, and $\mu$ an unramified charater.</p> <p><strong>My question</strong> is what if we replace the coefficient field to $E \neq Q_p$?</p> <p>In fact, at the end of the paper by Gerasimos Dousmanis <a href="http://arxiv.org/abs/0711.2137" rel="nofollow">"Rank two filtered $(φ, N)$-modules with Galois descent data and coefficients"</a>, the filtered $(\varphi, N)$ modules of all such 1-dim repns are all classified. My question really is, how do we write out the representations explicitly? </p> http://mathoverflow.net/questions/98103/1-dimensional-semi-stable-galois-representations-with-coefficients/98115#98115 Comment by 750am 750am 2012-05-28T04:35:20Z 2012-05-28T04:35:20Z Thank you very much！ http://mathoverflow.net/questions/98103/1-dimensional-semi-stable-galois-representations-with-coefficients Comment by 750am 750am 2012-05-27T13:30:58Z 2012-05-27T13:30:58Z @David, actually I also found that post, and am now looking at Conrad's paper, but I suspect if the paper has very &quot;explicit&quot; description of what the characters are...Do you know?