PAQ - Revision history

en>Joshua Issac: /* Hutter Prizes */ Euro -> €.

2014-06-27T10:41:59Z

Hutter Prizes: Euro -> €.

← Older revision		Revision as of 12:41, 27 June 2014
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	~~In [[number theory]], the '''Hasse norm theorem''' states that if L/K~~ is a ~~[[cyclic extension]] of [[number field]]s~~, ~~then if a nonzero element of K is a local norm everywhere~~, ~~then it is a global norm~~.		Luke is actually a superstar during the creating along with the job development initial next to his 3rd studio album, & , may be the resistant. He broken to the picture in 2005 along with his unique combination of down-residence accessibility, movie star very good appears and lyrics, is defined t inside a main way. The newest record Top about the country graph and #2 on the put graphs, creating it the 2nd maximum very first [http://www.banburycrossonline.com photos of luke bryan] billy currington tour, [http://www.hotelsedinburgh.org www.hotelsedinburgh.org], during those times of 2009 to get a country designer. <br><br>The child of your , knows determination and dedication are important elements in relation to an effective occupation- . His 1st record, Continue to be Me, made the best reaches “All My Buddies Say” and “Country Guy,” when his hard work, Doin’ Point, discovered the vocalist-3 right No. 2 single [http://lukebryantickets.pyhgy.com cheap luke bryan tickets] men and women: More Calling Is often a Good Point.”<br><br>During the tumble of 2015, Concerts: Luke And which had an impressive listing of , which include Urban. “It’s almost like you are obtaining a endorsement to visit to another level, states all those designers which were a part of the Concertsaround in to a greater measure of musicians.” It wrapped as among the most successful tours in their 15-year history.<br><br>my site; [http://lukebryantickets.lazintechnologies.com how to meet luke bryan]
	~~Here~~ to ~~be a global norm means to be an element ''k'' of K such that there is an element ''l'' of L~~ with ~~<math>\mathbf{N}_{L/K}(l) = k</math>; in other words ''k'' is a relative norm~~ of ~~some element of the extension field L. To be a local norm means that for some prime '''p''' of K~~ and ~~some prime '''P''' of L lying over K~~, ~~then ''k''~~ is a ~~norm from L<sub>'''P'''</sub>; here~~ the ~~"prime" '''p''' can be an archimedean valuation,~~ and the ~~theorem is a statement about completions in all valuations~~, ~~archimedean and non-archimedean~~.

	~~The theorem is no longer true in general if the extension is abelian but not cyclic~~. ~~A counter-example is given by the field <math>{\mathbf Q}(\sqrt{13}~~,~~\sqrt{17})~~/~~{\mathbf Q}<~~/~~math> where every rational square is~~ a ~~local norm everywhere but~~ <~~math~~>~~5^2~~<~~/math~~> ~~is not a global norm.~~

	~~This is an example~~ of ~~a theorem stating a [[local-global principle]]~~, and ~~is due~~ to ~~[[Helmut Hasse]]~~.

	~~The Hasse norm theorem can~~ be ~~deduced from~~ the ~~theorem that an element of~~ the ~~Galois cohomology group H<sup>~~2</~~sup>(''L''~~/~~''K'') is trivial if it is trivial locally everywhere, which is in turn equivalent to the deep theorem that the first cohomology of the idele class group vanishes~~. ~~This is true for all finite Galois extensions of number fields, not just cyclic ones~~. ~~For cyclic extensions the group~~ H<~~sup~~>2<~~/sup~~>~~(''L''/''K'') is isomorphic to~~ the ~~Tate cohomology group H<sup>0</sup>(''L''/''K'')~~ which ~~describes~~ which ~~elements~~ are ~~norms, so for cyclic extensions it becomes Hasse's theorem that an element is~~ a ~~norm if it is a local norm everywhere.~~

	~~==See also==~~

	*[[Grunwald–Wang theorem]], ~~about when an element that is~~ a ~~power everywhere locally is~~ a ~~power.~~

	~~==References==~~

	* H. Hasse, "A history of ~~class field theory", in [[J.W.S. Cassels]] and [[A. Frohlich]] (edd), ''Algebraic number theory'', [[Academic Press]], 1973~~. ~~Chap~~.~~XI.~~
	* G. Janusz, ''Algebraic number fields'', Academic Press, 1973. Theorem V.4.5, p. ~~156~~

	[~~[Category~~:~~Class field theory]]~~
	~~[[Category:Theorems in algebraic number theory]~~]

89.204.139.20: /* PAQ derivations */ cite web error (missing url=)

2013-12-28T13:09:37Z

PAQ derivations: cite web error (missing url=)

← Older revision		Revision as of 15:09, 28 December 2013
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	=~~= The strength~~ can be ~~imagined ==~~		In [[number theory]], the '''Hasse norm theorem''' states that if L/K is a [[cyclic extension]] of [[number field]]s, then if a nonzero element of K is a local norm everywhere, then it is a global norm.
			Here to be a global norm means to be an element ''k'' of K such that there is an element ''l'' of L with <math>\mathbf{N}_{L/K}(l) = k</math>; in other words ''k'' is a relative norm of some element of the extension field L. To be a local norm means that for some prime '''p''' of K and some prime '''P''' of L lying over K, then ''k'' is a norm from L<sub>'''P'''</sub>; here the "prime" '''p''' can be an archimedean valuation, and the theorem is a statement about completions in all valuations, archimedean and non-archimedean.

	, The ~~strength can be imagined, but there~~ is ~~a man behind Qin Yu Lan Shu unfathomable ground.<br>Court<br>stars out of four, Qin Yu and Li child girl, and love~~ the ~~クリスチャンルブタン偽物 lively Hou fee, plus black Qin Yu to follow~~.~~<br>After<br>Green Dragon Palace, clear water House, celestial domain, nine evil Hall, Zi Yan Fel クリスチャンルブタンサイズ~~ is ~~out four or five people, followed クリスチャンルブタン店舗~~ by ~~eight to feijian speed flight, and that eight out of the stars of the feijian Court, even fly directly toward~~ the ~~north to go.<br>~~<br>~~'also stars Court turned north~~, ~~is really amazing.' Dragon laughed.~~<~~br><br~~>~~now tied with eight feijian flight, is behind dozens of people, which in addition to dozens of people standing child girl,~~ every other individual's real strength, at least over all virtual hole late.<br><br>Qin Yu Sword flight, クリスチャンルブタンセール and クリスチャンルブタン値段 even children stand aside Royal Air flight speed was easy to follow the crowd.<br><br>'Li children, your speed ......' Qin Yu stunned.<br><br>Royal Air flight, this is ~~slower than the Sword flight on many,~~ but ~~Li child saver, even Royal Air flight.~~		The theorem is no longer true in general if the extension is abelian but not cyclic. A counter-example is given by the field <math>{\mathbf Q}(\sqrt{13},\sqrt{17})/{\mathbf Q}</math> where every rational square is a local norm everywhere but <math>5^2</math> is not a global norm.
	~~相关的主题文章：~~
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	<li>~~?aid=3~~</~~li>~~

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	~~== Forber come ==~~		This is an example of a theorem stating a [[local-global principle]], and is due to [[Helmut Hasse]].

	~~Its power, because it was complicated to a limit, so is~~ the ~~use~~ of ~~some low-grade rock gods lineup to be testing ground. '~~<br><br>'~~You mean~~, I should be FIGHTING test? how that test it?' Qin Yu heart began to think again.<br><br>black feather? Blue House? クリスチャンルブタンセール Wu He? Let them feel FIGHTING.<br><br>not!<br><br>have too much power in ~~battle formation, three seriously injured lost their lives how~~ to ~~do, クリスチャンルブタンメンズ通販 but other people can not waste time, after all, they are also to cultivate black ground.<br><br>Forber come?<br><br>Forber no soul,~~ the ~~soul~~ of ~~some attacks~~ is ~~essentially useless~~, ~~クリスチャンルブタン銀座 can~~ not ~~test FIGHTING power~~.<br><br>own experience FIGHTING power?<br><br>does not work, in the community of their own, although Jiang Lan can unscathed, if the force Jiang クリスチャンルブタンパンプス Lan sector クリスチャンルブタンアウトレット can use to ~~offset~~ the ~~attack space, then how test FIGHTING power it?~~<br><br>'~~Master~~, it is ~~very simple, and the old master science, casually looking for~~ a ~~robber forces gathering in the square, you arranged at some of the parties~~		The Hasse norm theorem can be deduced from the theorem that an element of the Galois cohomology group H<sup>2</sup>(''L''/''K'') is trivial if it is trivial locally everywhere, which is in turn equivalent to the deep theorem that the first cohomology of the idele class group vanishes. This is true for all finite Galois extensions of number fields, not just cyclic ones. For cyclic extensions the group H<sup>2</sup>(''L''/''K'') is isomorphic to the Tate cohomology group H<sup>0</sup>(''L''/''K'') which describes which elements are norms, so for cyclic extensions it becomes Hasse's theorem that an element is a norm if it is a local norm everywhere.
	~~相关的主题文章：~~
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	~~</ul>~~

	== ~~Yu Huang to think so~~ ==		==See also==

	~~Ten meters away completely negligible~~, ~~exudes~~ a ~~sharp Qijin between two parties troops, opposition to each other~~.~~<br><br>'Qin Yu~~, ~~you reach nine cents Emperor~~ of~~?' Yu Huang little face suddenly changed~~, ~~and he found himself only a vague feeling Qin Yu's strength, spirit realm and he~~ [~~http://www~~.~~lamartcorp~~.~~com/modules/mod_menu/rakuten_cl_13~~.~~php クリスチャンルブタン日本~~] ~~seemed almost~~.~~<br><br>~~'~~nine cents Emperor, be it.~~' ~~Qin Yu looked Yu Huang said.<br><br>Yu Huang to think so, Qin Yu would not be denied.<br><br>~~'~~how could that be? then reef yellow star battle you, but only reached level Emperor Xian~~, [~~http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_5.php クリスチャンルブタン店舗~~] ~~just open the third layer beasts spectrum can now ...... this [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_11.php クリスチャンルブタンブーツ~~] ~~for hundreds of years? you ..~~....' ~~Yu Wong and his face slightly pale .<br><br>insufficient millennium~~, ~~reached nine cents Emperor~~, ~~this is really horrible thing enough~~.~~<br><br>Qin Yu just smiling~~.~~<br><br>Qin Yu he did not say any of this cranky Yu Huang, Yu Huang Qin Yu soul realm and fairly~~. ~~Qin Yu could not clearly see through~~, this [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_1.php クリスチャンルブタン店舗東京] has been [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_11.php クリスチャンルブタン偽物] a series of speculation.~~<br><br>'Hey, you're the Yu Huang?' Hou Fei evil ruthless~~		*[[Grunwald–Wang theorem]], about when an element that is a power everywhere locally is a power.
	~~相关的主题文章：~~
	~~<ul>~~		==References==

	~~<li>~~[~~http~~:~~//www.ccins.org?q=node/2 http://www.ccins.org?q=node/2~~]~~</li>~~		* H. Hasse, "A history of class field theory", in [[J.W.S. Cassels]] and [[A. Frohlich]] (edd), ''Algebraic number theory'', [[Academic Press]], 1973. Chap.XI.
			* G. Janusz, ''Algebraic number fields'', Academic Press, 1973. Theorem V.4.5, p. 156
	~~<li>~~[~~http://www.liberalismen.dk/index.cgi http~~:~~//www.liberalismen.dk/index.cgi~~]~~</li>~~
			[[Category:Class field theory]]
	~~<li>[http://www.masuya06.com/cgi-bin/bbs/kutikomi_bbs.cgi http://www.masuya06.com/cgi-bin/bbs/kutikomi_bbs.cgi~~]~~</li>~~		[[Category:Theorems in algebraic number theory]]

	~~</ul>~~

en>XJDHDR at 17:40, 29 August 2012

2012-08-29T17:40:11Z

New page

== The strength can be imagined ==

, The strength can be imagined, but there is a man behind Qin Yu Lan Shu unfathomable ground. Court stars out of four, Qin Yu and Li child girl, and love the クリスチャンルブタン偽物 lively Hou fee, plus black Qin Yu to follow. After Green Dragon Palace, clear water House, celestial domain, nine evil Hall, Zi Yan Fel クリスチャンルブタンサイズ is out four or five people, followed クリスチャンルブタン店舗 by eight to feijian speed flight, and that eight out of the stars of the feijian Court, even fly directly toward the north to go. 'also stars Court turned north, is really amazing.' Dragon laughed. now tied with eight feijian flight, is behind dozens of people, which in addition to dozens of people standing child girl, every other individual's real strength, at least over all virtual hole late. Qin Yu Sword flight, クリスチャンルブタンセール and クリスチャンルブタン値段 even children stand aside Royal Air flight speed was easy to follow the crowd. 'Li children, your speed ......' Qin Yu stunned. Royal Air flight, this is slower than the Sword flight on many, but Li child saver, even Royal Air flight.
相关的主题文章：
<ul>

<li>?aid=3</li>

<li>

<li>?title=User:Awbiwgwyvl#like_ants_in_his_hands</li>

</ul>

== Forber come ==

Its power, because it was complicated to a limit, so is the use of some low-grade rock gods lineup to be testing ground. ' 'You mean, I should be FIGHTING test? how that test it?' Qin Yu heart began to think again. black feather? Blue House? クリスチャンルブタンセール Wu He? Let them feel FIGHTING. not! have too much power in battle formation, three seriously injured lost their lives how to do, クリスチャンルブタンメンズ通販 but other people can not waste time, after all, they are also to cultivate black ground. Forber come? Forber no soul, the soul of some attacks is essentially useless, クリスチャンルブタン銀座 can not test FIGHTING power. own experience FIGHTING power? does not work, in the community of their own, although Jiang Lan can unscathed, if the force Jiang クリスチャンルブタンパンプス Lan sector クリスチャンルブタンアウトレット can use to offset the attack space, then how test FIGHTING power it? 'Master, it is very simple, and the old master science, casually looking for a robber forces gathering in the square, you arranged at some of the parties
相关的主题文章：
<ul>

<li>?mod=space&uid=122850</li>

<li>?mod=space&uid=55276</li>

<li>?mod=space&uid=869039</li>

</ul>

== Yu Huang to think so ==

Ten meters away completely negligible, exudes a sharp Qijin between two parties troops, opposition to each other. 'Qin Yu, you reach nine cents Emperor of?' Yu Huang little face suddenly changed, and he found himself only a vague feeling Qin Yu's strength, spirit realm and he [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_13.php クリスチャンルブタン日本] seemed almost. 'nine cents Emperor, be it.' Qin Yu looked Yu Huang said. Yu Huang to think so, Qin Yu would not be denied. 'how could that be? then reef yellow star battle you, but only reached level Emperor Xian, [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_5.php クリスチャンルブタン店舗] just open the third layer beasts spectrum can now ...... this [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_11.php クリスチャンルブタンブーツ] for hundreds of years? you ......' Yu Wong and his face slightly pale . insufficient millennium, reached nine cents Emperor, this is really horrible thing enough. Qin Yu just smiling. Qin Yu he did not say any of this cranky Yu Huang, Yu Huang Qin Yu soul realm and fairly. Qin Yu could not clearly see through, this [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_1.php クリスチャンルブタン店舗東京] has been [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_11.php クリスチャンルブタン偽物] a series of speculation. 'Hey, you're the Yu Huang?' Hou Fei evil ruthless
相关的主题文章：
<ul>

<li>[http://www.ccins.org?q=node/2 http://www.ccins.org?q=node/2]</li>

<li>[http://www.liberalismen.dk/index.cgi http://www.liberalismen.dk/index.cgi]</li>

<li>[http://www.masuya06.com/cgi-bin/bbs/kutikomi_bbs.cgi http://www.masuya06.com/cgi-bin/bbs/kutikomi_bbs.cgi]</li>

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