Laurent Berger
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 Jan 17 comment De Rham cohomology of formal groups @Neil: that would be great, thank you! Jan 17 awarded Student Jan 17 asked De Rham cohomology of formal groups Jan 17 comment If Ramanujan's tau function has a prime power zero then $\ldots$ @Luis: Where in the proof of "if $\tau(p^n)=0$ then $\tau(p)=0$" (bottom of page 430 and top of page 431) is it assumed? Jan 17 comment If Ramanujan's tau function has a prime power zero then $\ldots$ @Luis: if I'm not mistaken, the proof of theorem 2 consists in showing that if $\tau(p^n)=0$ then $\tau(p)=0$ which does answer your question. Jan 17 answered If Ramanujan's tau function has a prime power zero then $\ldots$ Dec 31 comment The closures in $C^0(\mathbb{R}, \mathbb{R})$ of the set of integer valued polynomials, resp, of polynomials with integer coefficients @Paul: Hi Paul! I wrote a survey of Ferguson's results which you can find at the very bottom of this page umpa.ens-lyon.fr/~lberger/publications.html (it's in French, sorry). The main results are that if $K$ is a compact subset of $R$ then $Z[X]$ is discrete in $C^0(K,R)$ if the capacity of $K$ is $\geq 1$ and otherwise there is a finite set $J(K) \subset K$ such that a function $f$ is a limit of elements of $Z[X]$ if and only if there exists some $P(X) \in Z[X]$ such that $f(a)=P(a)$ for all $a \in J(K)$. For example if $K=[0,1]$ then $J(K)=\{0,1\}$. Dec 19 answered Induced representations and $(\varphi, \Gamma)-modules Dec 15 comment Explicitly describing a two-dimensional reducible representation of G_{Q_p} Although it's not very explicit, you can say that$H^1(G_{Q_p(\mu_{p^\infty})},Qp)$is a$\Lambda$-module and by the inflation-restriction map you character is in the part on which$\Gamma$acts by$\chi^j$. If you're wondering what$H^1(G_{Q_p(\mu_{p^\infty})},Qp)$looks like, the theory of$(\varphi,\Gamma)$-modules may help... Dec 9 awarded Critic Dec 7 answered Never appeared forthcoming papers Nov 7 answered What is the p-adic valuation of a number? Nov 4 comment What are the$p$-adic representations of$\hat{\mathbb{Z}}$? @Kevin: yes I think so! Just to recap: the continuous image of a compact set is compact so the image has to land in a compact subgroup of$GL_n(Q_p)$which we know is conjugate to a subgroup of$GL_n(Z_p)$. Conversely if$M = card(GL_n(F_p))$and$f(1)$is (say) in$GL_n(Z_p)$then for every$k$, the image of$p^{k-1}M Z$is in$1+p^k M_n(Z_p)$so the map from$Z$extends by uniform continuity. To relate this to Torsten's answer, it remains to check that a matrix is conjugate to an element of$GL_n(Z_p)\$ iff its char poly has integral coeffts. Nov 1 awarded Fanatic Oct 24 answered Can an etale (phi, Gamma) module be an extension of non-etale ones? Oct 24 comment Can an etale (phi, Gamma) module be an extension of non-etale ones? The last category is closed under extensions. What you mean is something different, isn't it? Oct 22 comment Citing papers that are in a language that you do not read. I don't think it's necessary to have read the whole paper in order to cite it, but you need to point to a precise result in the reference, and explain the translation between the result as it's stated, and the results as you use it. I find it annoying when I see stg like "by [6], we have..." when [6] is a book, especially when the author of the paper is unable to say where in the book the result is when you ask him. Oct 11 comment When should a result be made into a paper? @Kimball: Yes, Rota said that, see for instance: math.ohio-state.edu/~nevai/MYMATH/rota_ams_notices_01_97.html Oct 10 awarded Good Answer Oct 9 awarded Commentator