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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
Oct
9
comment Representation of vectors in $\mathbb{R}^2$ via differences of small vectors.
@André: yes indeed. Very nice. Problem solved!
Oct
6
comment Representation of vectors in $\mathbb{R}^2$ via differences of small vectors.
Indeed, Steinitz' theorem tells you about the radius of a disk centered at $0$ containing the partial sums, while fiktor's question is about the radius of a disk, possibly centered away from $0$, containing the partial sums.
Oct
5
comment Representation of vectors in $\mathbb{R}^2$ via differences of small vectors.
@Willie: Thank you for the reference!
Oct
5
answered Representation of vectors in $\mathbb{R}^2$ via differences of small vectors.
Sep
21
comment problems of subspace of M_n(C)
It's probably easier if the field is $\mathbb{C}$. For example take $k=n$ so the question is about subspaces such that any nonzero matrix is invertible. You see that any $2$-diml space of matrices contains noninvertible matrices (because if $A,B$ are two invertible matrices, then $\det(A+X \cdot B)$ has roots in $\mathbb{C}$). However, the corresponding problem over $\mathbb{R}$ is much harder, and is related to the maximal number of linearly independent vector fields on a sphere, which involves $K$-theory. See en.wikipedia.org/wiki/Vector_fields_on_spheres for details.
Aug
31
answered Numerical evidence of Beilinson's conjecture in local fields and function fields
Aug
25
awarded  Nice Answer
Aug
25
awarded  Editor
Aug
25
revised Refereeing a Paper
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