Comments for #angs@t / angs+ http://www.noncommutative.org antwerp noncommutative geometry seminar @ twitter / Google+ Sat, 21 Jan 2012 01:32:38 +0100 hourly 1 http://wordpress.org/?v=3.2.1 Comment on The algebraic closures of finite fields and their subfields by Omri F http://www.noncommutative.org/index.php/the-algebraic-closures-of-finite-fields-and-their-subfields.html#comment-447 Omri F Sat, 21 Jan 2012 01:32:38 +0000 http://www.noncommutative.org/?p=447#comment-447 It seems like the first union is wrong. Your index is i, but it is not used inside. It seems like the first union is wrong. Your index is i, but it is not used inside.

]]> Comment on On No and On by David Roberts http://www.noncommutative.org/index.php/on-no-and-on.html#comment-344 David Roberts Tue, 06 Dec 2011 23:32:49 +0000 http://www.noncommutative.org/?p=1215#comment-344 You've got a typo in your first bullet point: F_p^n instead of F_{p^n}. You’ve got a typo in your first bullet point: F_p^n instead of F_{p^n}.

]]> Comment on Water and cabbages in $\mathbb{F}_{1}$-geometry by theo http://www.noncommutative.org/index.php/water-and-cabbage-in-mathbbf_1-geometry.html#comment-318 theo Sun, 20 Nov 2011 21:49:04 +0000 http://www.noncommutative.org/?p=1103#comment-318 In my opinion, intuition comes from repeatedly experimenting with examples and/or getting used to things you notice in everyday life. If you get bored and start playing around with small (prime) numbers, you're bound to discover some sort of regularities: 1: 11, 31, 41, 61, 71 2: 2 3: 3, 13, 23, 43, 53, 73, 83 5: 5 7: 7, 17, 37, 47, 67, 97 9: 19, 29, 59, 79, 89 In this case, the hunch, gut feeling, intuition, or whatever you want to call it, is correct. It's in this sense, and only in this sense, that I proclaimed the result intuitive. In my opinion, intuition comes from repeatedly experimenting with examples and/or getting used to things you notice in everyday life. If you get bored and start playing around with small (prime) numbers, you’re bound to discover some sort of regularities:

1: 11, 31, 41, 61, 71
2: 2
3: 3, 13, 23, 43, 53, 73, 83
5: 5
7: 7, 17, 37, 47, 67, 97
9: 19, 29, 59, 79, 89

In this case, the hunch, gut feeling, intuition, or whatever you want to call it, is correct. It’s in this sense, and only in this sense, that I proclaimed the result intuitive.

]]> Comment on Water and cabbages in $\mathbb{F}_{1}$-geometry by pbelmans http://www.noncommutative.org/index.php/water-and-cabbage-in-mathbbf_1-geometry.html#comment-317 pbelmans Sun, 20 Nov 2011 20:12:12 +0000 http://www.noncommutative.org/?p=1103#comment-317 <blockquote>Specializing to the case $m=10$, you get the intuitive result that there are “as many” primes ending in $1$, as there are in $3$, $7$ and $9$ respectively.</blockquote> I can't find any intuitive reason for this result, could you elaborate on your reasons to expect this? I can't find any intuition in the opposite direction either, which might be seen as some intuition in the apparently correct direction, but if you can give me a stronger hunch I'd be a happy person :).

Specializing to the case $m=10$, you get the intuitive result that there are “as many” primes ending in $1$, as there are in $3$, $7$ and $9$ respectively.

I can’t find any intuitive reason for this result, could you elaborate on your reasons to expect this? I can’t find any intuition in the opposite direction either, which might be seen as some intuition in the apparently correct direction, but if you can give me a stronger hunch I’d be a happy person :) .

]]> Comment on Local Langlands correspondence by Maurizio Monge http://www.noncommutative.org/index.php/local-langlands-correspondence.html#comment-163 Maurizio Monge Fri, 21 Oct 2011 08:18:58 +0000 http://www.noncommutative.org/?p=678#comment-163 Ok, I guess you are referring to a case different from that talked at http://mathoverflow.net/questions/61773/p-adic-langlands-correspondence Ok, I guess you are referring to a case different from that talked at
http://mathoverflow.net/questions/61773/p-adic-langlands-correspondence

]]> Comment on Local Langlands correspondence by Kevin De Laet http://www.noncommutative.org/index.php/local-langlands-correspondence.html#comment-142 Kevin De Laet Wed, 19 Oct 2011 06:59:29 +0000 http://www.noncommutative.org/?p=678#comment-142 There's a proof of it in <i>The geometry and cohomology of some simple Shimura varieties</i> by M. Harris and R. Taylor. They proof it for any arbitrary finite extension of $\mathbb{Q}_p$. There’s a proof of it in The geometry and cohomology of some simple Shimura varieties by M. Harris and R. Taylor. They proof it for any arbitrary finite extension of $\mathbb{Q}_p$.

]]> Comment on Local Langlands correspondence by Maurizio Monge http://www.noncommutative.org/index.php/local-langlands-correspondence.html#comment-139 Maurizio Monge Tue, 18 Oct 2011 19:14:01 +0000 http://www.noncommutative.org/?p=678#comment-139 it has really been proved for any finite extension of $\mathbb{Q}_p$? I don't know about latest developments, but i don't recall that it was the case. it has really been proved for any finite extension of $\mathbb{Q}_p$? I don’t know about latest developments, but i don’t recall that it was the case.

]]> Comment on The $abc$-conjecture and some generalities by Constantin M. Petridi http://www.noncommutative.org/index.php/the-abc-conjecture-and-some-generalities.html#comment-102 Constantin M. Petridi Tue, 11 Oct 2011 08:05:32 +0000 http://www.noncommutative.org/?p=417#comment-102 I suggest you download the papers 1 Constantin M. Petridi, The abc-conjecture is true for at least $N(c), 1 leq N(c)<phi(c)/2$, partitions a,,b of c, arXiv: math/0301050. (See A. Nitaj's, ABC Conjecture Home Page). 2 " " A strong "abc-conjecture" for certain partitions a+b of c, arXiv: math/0511 224. 3 " " The number of equations c=a+b satisfying the abc-conjecture, arXiv: 0904.1935. The gist of above papers is that the geometric mean of the phi(c)/2 radicals R(abc) of the equations c=a+b, 0<a<b,, (a,b) = 1, is greater than K(epsilon) R(c)^(1-epsilon) c^2, where K(epsilon) an absolute positive constant, depending only on epsilon. Constantin M. Petridi I suggest you download the papers

1 Constantin M. Petridi, The abc-conjecture is true for at least
$N(c), 1 leq N(c)<phi(c)/2$, partitions
a,,b of c, arXiv: math/0301050. (See
A. Nitaj's, ABC Conjecture Home Page).

2 " " A strong "abc-conjecture" for certain
partitions a+b of c, arXiv: math/0511
224.

3 " " The number of equations c=a+b
satisfying the abc-conjecture, arXiv:
0904.1935.

The gist of above papers is that the geometric mean of the
phi(c)/2 radicals R(abc) of the equations c=a+b, 0<a<b,,
(a,b) = 1, is greater than K(epsilon) R(c)^(1-epsilon) c^2,
where K(epsilon) an absolute positive constant, depending only on epsilon.

Constantin M. Petridi

]]> Comment on The algebraic closures of finite fields and their subfields by Fredrik Meyer http://www.noncommutative.org/index.php/the-algebraic-closures-of-finite-fields-and-their-subfields.html#comment-101 Fredrik Meyer Mon, 10 Oct 2011 16:12:50 +0000 http://www.noncommutative.org/?p=447#comment-101 Interesting read! Seems like I stumble upon a lot of good math blogs these days. One comment: it is not "to proof" but "to prove" in English ;) Interesting read! Seems like I stumble upon a lot of good math blogs these days.

One comment: it is not “to proof” but “to prove” in English ;)

]]> Comment on The algebraic closures of finite fields and their subfields by Kevin De Laet http://www.noncommutative.org/index.php/the-algebraic-closures-of-finite-fields-and-their-subfields.html#comment-89 Kevin De Laet Sun, 09 Oct 2011 09:35:21 +0000 http://www.noncommutative.org/?p=447#comment-89 Bruno, ik heb alleen in het begin p vastgelegd, het is daarom dat ik heel de tijd met F_q zit te werken ipv met F_p om verwarring tegen te gaan. Niettemin, ik denk dat ik maar 1 keer p als index heb gebruikt, voor de rest heb ik p_i gebruikt. Ik heb het veranderd, als er nog dingen fout of verwarrend zijn, hoor ik het wel. Bruno, ik heb alleen in het begin p vastgelegd, het is daarom dat ik heel de tijd met F_q zit te werken ipv met F_p om verwarring tegen te gaan. Niettemin, ik denk dat ik maar 1 keer p als index heb gebruikt, voor de rest heb ik p_i gebruikt. Ik heb het veranderd, als er nog dingen fout of verwarrend zijn, hoor ik het wel.

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