P-adic gamma function - Revision history

en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

2014-09-25T13:23:11Z

References: replace mr template with mr parameter in CS1 templates; using AWB

← Older revision		Revision as of 15:23, 25 September 2014
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	~~In mathematics,~~ '~~''Tate duality''' or '''Poitou–Tate duality''' is~~ a ~~duality theorem for [[Galois cohomology]] groups of modules over the [[Galois group]] of an algebraic number field or [[local field]]~~, ~~introduced by {{harvs\|txt\|last=Tate\|author-link=John Tate\|year=1962}} and {{harvtxt\|Poitou\|1967}}~~.		I'm Alannah and I live in a seaside city in northern Germany, Blekendorf. I'm 31 and I'm will soon finish my study at Art History.<br><br>Feel free to visit my web page [http://www.youtube.fr/watch?v=xvwG79lFRKM Megapolis Hack]

	~~==Local Tate duality==~~

	~~{{main\|local Tate duality}}~~
	~~Local Tate duality says there is a perfect pairing of finite groups~~
	~~:<math>\displaystyle H^r(k,M)\times H^{2-r}(k,M~~'~~)\rightarrow H^2(k,G_m)=Q/Z</math>~~

	~~where ''M'' is a finite group scheme~~ and '~~'M''′ its dual Hom(''M'',''G~~<~~sub~~>m<~~/sub~~>~~'').~~

	~~==See also==~~

	*[[~~Artin–Verdier duality]]~~
	*[[Tate pairing]]

	~~==References==~~

	*{{Citation \| last1=Haberland \| first1=Klaus \| title=Galois cohomology of algebraic number fields \| url=http://~~books~~.~~google~~.~~com~~/~~books~~?id=~~PwbvAAAAMAAJ \| publisher=VEB Deutscher Verlag der Wissenschaften \| id={{MR\|519872}} \| year=1978}}~~
	*{{Citation \| last1=Poitou \| first1=Georges \| title=Cohomologie galoisienne des modules finis \| url=http://books.google.com/books?id=E3GmAAAAIAAJ \| publisher=Dunod \| location=Paris \| series=Séminaire de l'Institut de Mathématiques de Lille, sous la direction de G. Poitou. Travaux et Recherches Mathématiques, \| id={{MR\|0219591}} \| year=1967 \| volume=13 \| chapter=Propriétés globales des modules finis \| pages=255–277}}
	*{{Citation \| last1=Tate \| first1=John \| author1-link=John Tate \| title=Proceedings of the International Congress of Mathematicians (Stockholm, 1962) \| url=http://mathunion.org/ICM/ICM1962.1/ \| publisher=Inst. Mittag-Leffler \| location=Djursholm \| id={{MR\|0175892}} \| year=1963 \| chapter=Duality theorems in Galois cohomology over number fields \| pages=288–295}}

	~~[[Category:Algebraic number theory]]~~
	~~[[Category:Galois theory]~~]

194.78.35.195: wikify

2012-11-21T16:15:38Z

wikify

← Older revision		Revision as of 18:15, 21 November 2012
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			In mathematics, '''Tate duality''' or '''Poitou–Tate duality''' is a duality theorem for [[Galois cohomology]] groups of modules over the [[Galois group]] of an algebraic number field or [[local field]], introduced by {{harvs\|txt\|last=Tate\|author-link=John Tate\|year=1962}} and {{harvtxt\|Poitou\|1967}}.

			==Local Tate duality==

	~~A civil rights organization on Thursday demanded~~ a ~~meeting with the CEO~~ of ~~[http~~://photobucket.com/images/Barneys Barneys] New York and threatened to picket the luxury department store in Manhattan after two black customers said they were stopped by police after making expensive purchases.<br>~~<br>Trayon Christian~~, 19, of Queens said after he bought a $349 Ferragamo belt on April 29 he was handcuffed and detained for two hours before being released with no charges. He filed a discrimination lawsuit against Barneys and the New York City Police Department on Monday.<br><br>Undercover police swarmed Kayla Phillips, 21, of Brooklyn at a subway station and demanded to see her credit card after she left Barneys with her purchase of a $2,~~500 [http:~~//~~www.pcs-systems.co.uk/Images/celinebag.aspx Celine UK] purse on Feb. 28, said her lawyer Kareem Vessup.<br~~>~~Phillips,~~ a ~~nursing student, had received a tax return~~ and ~~decided to splurge on the designer purse~~, ~~Vessup said.~~<br><br>~~She filed notice of an upcoming lawsuit against the NYPD and plans to sue Barneys, he said~~.~~<br>In his lawsuit, Christian, a mechanical engineering student, said when he bought the belt, Barneys telephoned police to report a criminal act. When he stepped out~~ of ~~the store with his shopping bag, he was handcuffed on the sidewalk and brought to the 19th Precinct, the lawsuit said~~.<br><br>Police interrogated him "as to how a young black man such as himself could afford to purchase such an expensive belt and that the debit card he had in his possession had to be fake," the lawsuit said.~~<br>Michael Palillo, a lawyer representing Christian, said his client had saved up earnings from a work-study program at New York City College of Technology and was [~~http://~~answers~~.~~yahoo~~.com/~~search/search_result~~?p=~~excited&submit-go~~=~~Search+Y!+Answers excited] to treat himself to a trendy belt he~~'~~d admired on some of the rappers he follows on television~~.~~<br><br>"He enjoys fashion," Palillo said~~.~~<br>The racial profiling incident violated his civil rights~~, ~~said~~ the ~~lawsuit, which was filed in state Supreme Court in Manhattan and seeks unspecified damages.<br>Barneys on its Facebook page said "no employee~~ of Barneys" was involved and it "has zero tolerance for any form of discrimination and we stand by our long history in support of all human rights."<br><br>The NYPD did not immediately respond to a request for comment.<br>National Action Network, ~~a civil rights group led by Reverend Al Sharpton, said it was mobilizing activists to take direct action against the store and the NYPD~~.~~<br>"National Action Network will immediately demand a meeting with the Barneys New York CEO," NAN spokeswoman Rachel Noerdlinger said in a statement~~.~~<br><br>The group is "planning to picket the store if the pattern of racial profiling is not immediately rectified after numerous incidents of discrimination have come to light," Noerdlinger said~~.~~<br>The incidents came to light little more than two months after a judge ruled the NYPD discriminated against black and Hispanic youths~~ in its controversial stop-and-frisk crime fighting tactic.<br><br>On its website, Barneys describes itself as "... a mecca for discerning fashionistas and clothing connoisseurs since 1923" and quotes "Sex and the City" actress Sarah Jessica Parker as telling Vanity Fair, "If you're a nice person and you work hard, you get to go shopping at Barneys. It's the decadent reward."<br><br>(Additional reporting by Luke Swiderski; editing by Gunna Dickson)		{{main\|local Tate duality}}
			Local Tate duality says there is a perfect pairing of finite groups
			:<math>\displaystyle H^r(k,M)\times H^{2-r}(k,M')\rightarrow H^2(k,G_m)=Q/Z</math>

			where ''M'' is a finite group scheme and ''M''′ its dual Hom(''M'',''G<sub>m</sub>'').

			==See also==

			*[[Artin–Verdier duality]]
			*[[Tate pairing]]

			==References==

			*{{Citation \| last1=Haberland \| first1=Klaus \| title=Galois cohomology of algebraic number fields \| url=http://books.google.com/books?id=PwbvAAAAMAAJ \| publisher=VEB Deutscher Verlag der Wissenschaften \| id={{MR\|519872}} \| year=1978}}
			*{{Citation \| last1=Poitou \| first1=Georges \| title=Cohomologie galoisienne des modules finis \| url=http://books.google.com/books?id=E3GmAAAAIAAJ \| publisher=Dunod \| location=Paris \| series=Séminaire de l'Institut de Mathématiques de Lille, sous la direction de G. Poitou. Travaux et Recherches Mathématiques, \| id={{MR\|0219591}} \| year=1967 \| volume=13 \| chapter=Propriétés globales des modules finis \| pages=255–277}}
			*{{Citation \| last1=Tate \| first1=John \| author1-link=John Tate \| title=Proceedings of the International Congress of Mathematicians (Stockholm, 1962) \| url=http://mathunion.org/ICM/ICM1962.1/ \| publisher=Inst. Mittag-Leffler \| location=Djursholm \| id={{MR\|0175892}} \| year=1963 \| chapter=Duality theorems in Galois cohomology over number fields \| pages=288–295}}

			[[Category:Algebraic number theory]]
			[[Category:Galois theory]]

en>Michael Hardy: /* Definition */

2011-11-28T18:13:45Z

Definition

New page

A civil rights organization on Thursday demanded a meeting with the CEO of [http://photobucket.com/images/Barneys Barneys] New York and threatened to picket the luxury department store in Manhattan after two black customers said they were stopped by police after making expensive purchases. Trayon Christian, 19, of Queens said after he bought a $349 Ferragamo belt on April 29 he was handcuffed and detained for two hours before being released with no charges. He filed a discrimination lawsuit against Barneys and the New York City Police Department on Monday. Undercover police swarmed Kayla Phillips, 21, of Brooklyn at a subway station and demanded to see her credit card after she left Barneys with her purchase of a $2,500 [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine UK] purse on Feb. 28, said her lawyer Kareem Vessup. Phillips, a nursing student, had received a tax return and decided to splurge on the designer purse, Vessup said. She filed notice of an upcoming lawsuit against the NYPD and plans to sue Barneys, he said. In his lawsuit, Christian, a mechanical engineering student, said when he bought the belt, Barneys telephoned police to report a criminal act. When he stepped out of the store with his shopping bag, he was handcuffed on the sidewalk and brought to the 19th Precinct, the lawsuit said. Police interrogated him "as to how a young black man such as himself could afford to purchase such an expensive belt and that the debit card he had in his possession had to be fake," the lawsuit said. Michael Palillo, a lawyer representing Christian, said his client had saved up earnings from a work-study program at New York City College of Technology and was [http://answers.yahoo.com/search/search_result?p=excited&submit-go=Search+Y!+Answers excited] to treat himself to a trendy belt he'd admired on some of the rappers he follows on television. "He enjoys fashion," Palillo said. The racial profiling incident violated his civil rights, said the lawsuit, which was filed in state Supreme Court in Manhattan and seeks unspecified damages. Barneys on its Facebook page said "no employee of Barneys" was involved and it "has zero tolerance for any form of discrimination and we stand by our long history in support of all human rights." The NYPD did not immediately respond to a request for comment. National Action Network, a civil rights group led by Reverend Al Sharpton, said it was mobilizing activists to take direct action against the store and the NYPD. "National Action Network will immediately demand a meeting with the Barneys New York CEO," NAN spokeswoman Rachel Noerdlinger said in a statement. The group is "planning to picket the store if the pattern of racial profiling is not immediately rectified after numerous incidents of discrimination have come to light," Noerdlinger said. The incidents came to light little more than two months after a judge ruled the NYPD discriminated against black and Hispanic youths in its controversial stop-and-frisk crime fighting tactic. On its website, Barneys describes itself as "... a mecca for discerning fashionistas and clothing connoisseurs since 1923" and quotes "Sex and the City" actress Sarah Jessica Parker as telling Vanity Fair, "If you're a nice person and you work hard, you get to go shopping at Barneys. It's the decadent reward." (Additional reporting by Luke Swiderski; editing by Gunna Dickson)