Lanczos algorithm - Revision history

en>Mehr86 at 20:01, 5 December 2014

2014-12-05T20:01:12Z

← Older revision		Revision as of 22:01, 5 December 2014
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	A '~~''Chevalley scheme''' in~~ [~~[algebraic geometry]] was a precursor notion of [[scheme theory]]~~.		Alyson is what my husband loves to contact me but I don't like [http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies online psychic] psychic readings ([https://www-ocl.gist.ac.kr/work/xe/?document_srl=605236 you could try here]) when individuals use my full name. Credit authorising is how he tends to make cash. The favorite pastime for him and his kids is to play lacross and he would by no means give it up. For a whilst I've been in Mississippi but now I'm considering other choices.<br><br>Also visit my homepage email psychic readings ([http://www.publicpledge.com/blogs/post/7034 www.publicpledge.com])

	~~Let ''X'' be a separated integral [[noetherian scheme]], ''R'' its [[function field of an algebraic variety\|function field]]~~. ~~If we denote by <math>X'<~~/~~math> the set of subrings <math>\mathcal O_x<~~/~~math> of ''R'', where ''x'' runs through ''X''~~ (~~when <math>X=\mathrm{Spec}(A)<~~/~~math>, we denote <math>X'<~~/~~math> by <math>L(A)<~~/~~math>), <math>X'<~~/~~math> verifies the following three properties~~
	* For each <math>M\in X' </~~math>, ''R''~~ is ~~the field of fractions of ''M''~~.
	* There is ~~a finite set of noetherian subrings <math>A_i</math> of ''R'' so that <math>X'=\cup_i L(A_i) </math>~~ and ~~that, for each pair of indices ''i,j'', the subring <math>A_{ij} </math> of ''R'' generated~~ by ~~<math> A_i \cup A_j </math> is an <math>A_i</math>-algebra of finite type~~.
	* If <math>M\subseteq N</math> in <math>X'~~</math> are such that the maximal ideal of ''M'' is contained~~ in ~~that of ''N'', then ''M=N'~~'.

	~~Originally, [[Chevalley]] also supposed that R was an extension of finite type of a field K and that the~~ <~~math~~> ~~A_i~~ <~~/math~~>~~'s were algebras of finite type over a field too~~ (~~this simplifies the second condition above).~~

	~~==Bibliography==~~

	*{{cite journal
	~~\| last = Grothendieck~~
	~~\| first = Alexandre~~
	~~\| authorlink = Alexandre Grothendieck~~
	~~\| coauthors = [[Jean Dieudonné]]~~
	~~\| year = 1960~~
	~~\| title = [[Éléments de géométrie algébrique]]~~
	~~\| volume = I. Le langage des schémas~~
	~~\| journal = [[Publications Mathématiques de l'IHÉS]]~~
	~~\| pages = I.8~~
	~~<!-- Please do not add url field as the template cannot handle a title with both an external link and a wikilink. -->~~
	}} [http://www.~~numdam~~.~~org:80~~/~~numdam-bin~~/~~feuilleter?id=PMIHES_1960__4_ Online]~~


	~~[[Category:Scheme theory]~~]

en>Monkbot: /* Applications */Fix CS1 deprecated date parameter errors

2014-01-24T09:50:22Z

Applications: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 11:50, 24 January 2014
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	~~Hi there~~, ~~I am Alyson Pomerleau and I believe it sounds fairly great~~ when ~~you say it~~. ~~What I adore performing~~ is ~~football but I don~~'~~t have~~ the ~~time recently~~. ~~Ohio is where her home~~ is. ~~She functions as~~ a ~~journey agent but soon she'll be on her personal.~~<br><br>~~My page :: clairvoyance~~ [[http://~~bigpolis~~.~~com~~/~~blogs~~/~~post/6503 simply click the following internet page~~]]		A '''Chevalley scheme''' in [[algebraic geometry]] was a precursor notion of [[scheme theory]].

			Let ''X'' be a separated integral [[noetherian scheme]], ''R'' its [[function field of an algebraic variety\|function field]]. If we denote by <math>X'</math> the set of subrings <math>\mathcal O_x</math> of ''R'', where ''x'' runs through ''X'' (when <math>X=\mathrm{Spec}(A)</math>, we denote <math>X'</math> by <math>L(A)</math>), <math>X'</math> verifies the following three properties
			* For each <math>M\in X' </math>, ''R'' is the field of fractions of ''M''.
			* There is a finite set of noetherian subrings <math>A_i</math> of ''R'' so that <math>X'=\cup_i L(A_i) </math> and that, for each pair of indices ''i,j'', the subring <math>A_{ij} </math> of ''R'' generated by <math> A_i \cup A_j </math> is an <math>A_i</math>-algebra of finite type.
			* If <math>M\subseteq N</math> in <math>X'</math> are such that the maximal ideal of ''M'' is contained in that of ''N'', then ''M=N''.

			Originally, [[Chevalley]] also supposed that R was an extension of finite type of a field K and that the <math> A_i </math>'s were algebras of finite type over a field too (this simplifies the second condition above).

			==Bibliography==

			*{{cite journal
			\| last = Grothendieck
			\| first = Alexandre
			\| authorlink = Alexandre Grothendieck
			\| coauthors = [[Jean Dieudonné]]
			\| year = 1960
			\| title = [[Éléments de géométrie algébrique]]
			\| volume = I. Le langage des schémas
			\| journal = [[Publications Mathématiques de l'IHÉS]]
			\| pages = I.8
			<!-- Please do not add url field as the template cannot handle a title with both an external link and a wikilink. -->
			}} [http://www.numdam.org:80/numdam-bin/feuilleter?id=PMIHES_1960__4_ Online]


			[[Category:Scheme theory]]

en>Rgdboer: /* The algorithm */ update link

2012-08-08T00:02:36Z

The algorithm: update link

New page

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