en>Yobot: clean up, References after punctuation per WP:REFPUNC and WP:CITEFOOT using AWB (8797)

2012-12-11T17:48:49Z

clean up, References after punctuation per WP:REFPUNC and WP:CITEFOOT using AWB (8797)

← Older revision		Revision as of 19:48, 11 December 2012
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	~~It involves expertise and knowledge~~ of ~~various tools and technologies used for creating websites. Also, you may want to opt for~~ a ~~more professioanl theme if you are planning~~ on ~~showing your site off to~~ a ~~high volume~~ of ~~potential customers each day. * A community forum for debate~~ of ~~the product together with some other customers in the comments spot~~. ~~Keep reading for some great Word~~ - ~~Press ideas you can start using today. The number of options offered here~~ is ~~overwhelming~~, ~~but once I took the time to begin to review the video training, I was amazed at how easy~~ it ~~was to create a squeeze page and~~ a ~~membership site.~~ <br><br>		In [[number theory]], a '''cyclotomic character''' is a [[Character (mathematics)#Multiplicative character\|character]] of a [[Galois group]] giving the Galois [[Group action\|action]] on a [[Group (mathematics)\|group]] of [[roots of unity]]. As a one-dimensional [[Group representation\|representation]] over a [[Ring (mathematics)\|ring]] ''R'', its [[representation space]] is generally denoted by ''R''(1) (that is, it is a representation {{nowrap\|χ : ''G'' → Aut<sub>R</sub>(''R''(1)) ≈ GL(1, ''R'')}}).

	~~Choosing what kind~~ of ~~links you~~'~~ll be using~~ is a ~~ctitical aspect~~ of ~~any linkwheel strategy, especially since there are several different types~~ of ~~links that are assessed by search engines~~. ~~You do not catch~~ a ~~user~~'~~s attention through big and large pictures that usually takes~~ a ~~millennium~~ to ~~load up~~. ~~This may possibly also permit it currently being seriously straightforward~~ to ~~modify~~ the ~~hues within your Ad - Sense code so~~ the ~~ads blend nicely with~~ the ~~many term broad internet word wide web web page in case you can come to your conclusion to run~~ the ~~adverts. By purchasing Word - Press weblogs you can acquire your very own domain title and have total command~~ of ~~your web site~~. ~~By using Word~~ - ~~Press~~, ~~you can develop very rich~~, ~~user~~-~~friendly and full-functional website~~. <br><br>~~Usually, Wordpress owners selling~~ the ad space on ~~monthly basis~~ and ~~this means a residual income source~~. ~~Note: at~~ a ~~first glance WP Mobile Pro themes do not appear to be glamorous or fancy. I've applied numerous Search engine optimization~~-~~ready Word~~ - ~~Press themes and I can say~~ from ~~knowledge that I consider~~ the ~~Genesis Search engine marketing panel one particular~~ of the ~~simplest~~ to use. ~~The first thing you need~~ to do is ~~to choose~~ the ~~right web hosting plan~~. ~~After that~~ the ~~developer adds~~ the ~~unordered list for navigations~~. <br><br>~~Google Maps Excellent navigation feature with Google Maps and latitude, for letting people who have access to your account Latitude know exactly where you are~~. In ~~case you need to hire PHP developers or hire Offshore Code~~ - ~~Igniter development services or you are looking for Word~~ - ~~Press development experts then Mindfire Solutions would~~ be the ~~right choice for~~ a ~~Software Development partner. This allows for keeping~~ the ~~content editing toolbar in place at all times no matter how far down the page is scrolled. If you are you looking for more information regarding~~ [~~http~~://~~aorta~~.~~in/WordpressDropboxBackup37844 backup plugin~~] ~~stop by~~ the ~~site~~. ~~Giant business organizations can bank on enterprise solutions to incorporate latest web technologies such as content management system etc~~, ~~yet some are looking for economical solutions. Wordpress template~~ is ~~loaded with lots~~ of ~~prototype that unite graphic features and content area.~~ <br><br>~~You will know which~~ of ~~your Word~~ - ~~Press blog posts are attracting more unique visitors which in turn will help you develop better products and services for your customers~~. ~~In fact portfolio Word~~ - ~~Press themes is a smooth~~ and ~~attractive but considerably flawed Word~~ - ~~Press theme~~ in ~~creating simpler to the photographers or designers to develop a specific internet site showcasing their most current perform since it appear modern~~-~~day and has fantastic typography and large photographs which would develop an attractive wanting portfolio internet site~~. ~~While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget~~. ~~Word~~ - ~~Press~~ is the ~~most popular personal publishing platform which was launched in 2003~~. ~~Press CTRL and the numbers one to six to choose your option~~.		==<span id="padic"></span>''p''-adic cyclotomic character==
			If ''p'' is a [[prime number\|prime]], and ''G'' is the [[absolute Galois group]] of the [[rational number]]s, the '''''p''-adic cyclotomic character''' is a [[group homomorphism]]

			:<math>\chi_p:G\rightarrow\mathbf{Z}_p^\times</math>

			where '''Z'''<sub>''p''</sub><sup>×</sup> is the [[group of units]] of the ring of [[p-adic integers]]. This homomorphism is defined as follows. Let ''ζ''<sub>''n''</sub> be a [[Primitive root of unity\|primitive]] ''p''<sup>''n''</sup> root of unity. Every ''p''<sup>''n''</sup> root of unity is a power of ''ζ''<sub>''n''</sub> uniquely defined as an element of the ring of integers modulo ''p''<sup>''n''</sup>. Primitive roots of unity correspond to the [[Multiplicative group of integers modulo n\|invertible elements]], i.e. to ('''Z'''/''p''<sup>''n''</sup>)<sup>×</sup>. An element ''g'' of the Galois group ''G'' sends ''ζ''<sub>''n''</sub> to another primitive ''p''<sup>''n''</sup> root of unity

			:<math>\theta=\zeta_n^{a_{g,n}}</math>

			where ''a''<sub>''g'',''n''</sub> ∈ ('''Z'''/''p''<sup>''n''</sup>)<sup>×</sup>. For a given ''g'', as ''n'' varies, the ''a''<sub>''g'',''n''</sub> form a comptatible system in the sense that they give an element of the [[inverse limit]] of the ('''Z'''/''p''<sup>''n''</sup>)<sup>×</sup>, which is '''Z'''<sub>p</sub><sup>×</sup>. Therefore, the ''p''-adic cyclotomic character sends ''g'' to the system (''a''<sub>''g'',''n''</sub>)<sub>''n''</sub>, thus encoding the action of ''g'' on all ''p''-power roots of unity.

			In fact, <math>\chi_p</math> is a [[Continuous function\|continuous]] homomorphism (where the [[topological space\|topology]] on ''G'' is the [[Krull topology]], and that on '''Z'''<sub>''p''</sub><sup>×</sup> is the [[p-adic]] topology).

			==As a compatible system of ℓ-adic representations==
			By varying ℓ over all prime numbers, a [[compatible system of ℓ-adic representations]] is obtained from the ℓ-adic cyclotomic characters (when considering compatible systems of representations, the standard terminology is to use the symbol ℓ to denote a prime instead of ''p''). That is to say, χ = { χ<sub>ℓ</sub> }<sub>ℓ</sub> is a "family" of ℓ-adic representations

			:<math>\chi_\ell:G_\mathbf{Q}\rightarrow\operatorname{GL}_1(\mathbf{Z}_\ell)</math>

			satisfying certain compatibilities between different primes. In fact, the χ<sub>ℓ</sub> form a [[strictly compatible system of ℓ-adic representations]].

			==Geometric realizations== <!-- Note: Tate motive redirects here -->
			The ''p''-adic cyclotomic character is the ''p''-adic [[Tate module]] of the [[Algebraic torus\|multiplicative group scheme]] '''G'''<sub>''m'','''Q'''</sub> over '''Q'''. As such, its representation space can be viewed as the [[inverse limit]] of the groups of ''p''<sup>''n''</sup>th roots of unity in {{Overline\|'''Q'''}}.

			In terms of [[étale cohomology\|cohomology]], the ''p''-adic cyclotomic character is the [[Duality (mathematics)\|dual]] of the first ''p''-adic [[étale cohomology]] group of '''G'''<sub>''m''</sub>. It can also be found in the étale cohomology of a [[projective variety]], namely the [[projective line]]: it is the dual of ''H''<sup>2</sup><sub>ét</sub>( '''P'''<sup>1</sup> ).

			In terms of [[Motive (algebraic geometry)\|motives]], the ''p''-adic cyclotomic character is the ''p''-adic realization of the '''Tate motive''' '''Z'''(1). As a [[Grothendieck motive]], the Tate motive is the dual of ''H''<sup>2</sup>( '''P'''<sup>1</sup> ).<ref>Section 3 of {{Citation
			\| last=Deligne
			\| first=Pierre
			\| author-link=Pierre Deligne
			\| contribution=Valeurs de fonctions ''L'' et périodes d'intégrales
			\| contribution-url=http://www.ams.org/online_bks/pspum332/pspum332-ptIV-8.pdf
			\| title=Automorphic Forms, Representations, and L-Functions
			\| editor-last=Borel
			\| editor-first=Armand
			\| editor-link=Armand Borel
			\| editor2-last=Casselman
			\| editor2-first=William
			\| publisher=[[American Mathematical Society\|AMS]]
			\| location=Providence, RI
			\| series=Proceedings of the Symposium in Pure Mathematics
			\| isbn=0-8218-1437-0
			\| mr=0546622 \| zbl=0449.10022
			\| year=1979
			\| volume=33.2
			\| page=325
			\| language=French}}
			</ref>

			==Properties==
			The ''p''-adic cyclotomic character satisfies several nice properties.

			*It is [[unramified]] at all primes ℓ ≠ ''p'' (i.e. the [[inertia subgroup]] at ℓ acts trivially).
			*If Frob<sub>ℓ</sub> is a [[Frobenius element]] for ℓ ≠ ''p'', then χ<sub>p</sub>(Frob<sub>ℓ</sub>) = ℓ
			*It is [[Crystalline_representation\|crystalline]] at ''p''.

			==See also==
			*[[Tate twist]]

			==References==
			{{reflist}}

			[[Category:Algebraic number theory]]

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-06T00:23:00Z

ISBNs (Build KC)

New page

It involves expertise and knowledge of various tools and technologies used for creating websites. Also, you may want to opt for a more professioanl theme if you are planning on showing your site off to a high volume of potential customers each day. * A community forum for debate of the product together with some other customers in the comments spot. Keep reading for some great Word - Press ideas you can start using today. The number of options offered here is overwhelming, but once I took the time to begin to review the video training, I was amazed at how easy it was to create a squeeze page and a membership site. 

Choosing what kind of links you'll be using is a ctitical aspect of any linkwheel strategy, especially since there are several different types of links that are assessed by search engines. You do not catch a user's attention through big and large pictures that usually takes a millennium to load up. This may possibly also permit it currently being seriously straightforward to modify the hues within your Ad - Sense code so the ads blend nicely with the many term broad internet word wide web web page in case you can come to your conclusion to run the adverts. By purchasing Word - Press weblogs you can acquire your very own domain title and have total command of your web site. By using Word - Press, you can develop very rich, user-friendly and full-functional website. Usually, Wordpress owners selling the ad space on monthly basis and this means a residual income source. Note: at a first glance WP Mobile Pro themes do not appear to be glamorous or fancy. I've applied numerous Search engine optimization-ready Word - Press themes and I can say from knowledge that I consider the Genesis Search engine marketing panel one particular of the simplest to use. The first thing you need to do is to choose the right web hosting plan. After that the developer adds the unordered list for navigations. Google Maps Excellent navigation feature with Google Maps and latitude, for letting people who have access to your account Latitude know exactly where you are. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. If you are you looking for more information regarding [http://aorta.in/WordpressDropboxBackup37844 backup plugin] stop by the site. Giant business organizations can bank on enterprise solutions to incorporate latest web technologies such as content management system etc, yet some are looking for economical solutions. Wordpress template is loaded with lots of prototype that unite graphic features and content area. You will know which of your Word - Press blog posts are attracting more unique visitors which in turn will help you develop better products and services for your customers. In fact portfolio Word - Press themes is a smooth and attractive but considerably flawed Word - Press theme in creating simpler to the photographers or designers to develop a specific internet site showcasing their most current perform since it appear modern-day and has fantastic typography and large photographs which would develop an attractive wanting portfolio internet site. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. Word - Press is the most popular personal publishing platform which was launched in 2003. Press CTRL and the numbers one to six to choose your option.

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en>Yobot: clean up, References after punctuation per WP:REFPUNC and WP:CITEFOOT using AWB (8797)

en>Helpful Pixie Bot: ISBNs (Build KC)