en>Yobot: Tagging + other fixes, added orphan tag using AWB (10392)

2014-08-21T19:49:27Z

Tagging + other fixes, added orphan tag using AWB (10392)

en>BattyBot: removed Template:Multiple issues & general fixes using AWB (8686)

2012-12-02T22:12:26Z

removed Template:Multiple issues & general fixes using AWB (8686)

← Older revision		Revision as of 00:12, 3 December 2012
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	~~Most evaporated coolers have~~ a ~~tendency to be relatively heavy and slightly bulky which can make them tough to carry about from room to room~~. ~~The contenders have been~~ a ~~soft-side model from Kelty~~, the ~~affordable and hugely portable Folding Cooler (58 quarts~~, ~~$45~~.~~95) a pricey pro~~-~~level” icebox from Yeti~~, the ~~Tundra 45 model (45 quarts~~, ~~$329)~~ and a ~~enormous tank made~~ by ~~Igloo,~~ the ~~Yukon 70 (70 quarts, $389.99), which touts Keeps Cold For 7 Days” right~~ on ~~its lid. In~~ the ~~August heat no cooler lasted for additional than 4 days. We stocked 10 pounds~~ of ~~ice in each and every and let~~ the ~~sun and hot air do its worst.~~<br><br>~~Coleman Xtreme or Ultimate Xtreme coolers — that~~'s ~~what we utilised and block ice lasted 7 days in 90+ degree heat~~ (~~and~~ the ~~cooler sat in a parked vehicle significantly~~ of the ~~time~~, so it ~~was even hotter)~~, ~~despite~~ the ~~fact that I did pile blankets and tarps more than~~ the ~~cooler and kept a separate cooler for drinks~~. ~~Igloo Maxcold coolers —~~ the ~~Maxcold” name has some smaller sized coolers~~, ~~soft-sided coolers~~ and ~~ones without insulated tops~~ that ~~are NOT what you need. Does not incorporate a CPU Cooler~~.<br><br>~~No ice necessary to preserve meals~~ and ~~snacks at~~ the ~~fantastic temperature~~, ~~so you can have a lot more area for actual food~~ and ~~drink~~. ~~With a lengthy road trip ahead~~, ~~no matter whether you have got small ones with you or not~~, ~~auto coolers can make points significantly easier. When we reviewed~~ the ~~Hyper 212 Evo in our January 2012 problem~~, ~~we had~~ two ~~important complaints about it: The backplate mounting procedure remained annoying~~, ~~and~~ the ~~cooler did not have LGA2011 mounting assistance.~~<br><br>~~When you have almost any questions about wherever~~ and ~~tips~~ on ~~how to work with [~~http://www.~~bestcoolerreviewshq~~.~~com~~/~~best-cooler-for-the-money~~/ ~~Www~~.~~bestcoolerreviewshq~~.~~Com~~], ~~you can e mail us at~~ the ~~website. In order to differentiate in between lower~~-~~finish and larger-end models~~, ~~Igloo and Coleman What Is The Greatest Cooler For The Revenue~~ (~~among other folks~~) ~~have adopted a technique of naming and advertising their coolers following~~ the ~~length~~ of ~~time they can hold some thing cold. It relies on draining and weighing~~ the ~~quantity~~ of ~~meltwater made at regular measurement told us~~ the ~~percentage of ice that had melted up to that point~~ in ~~time~~. ~~In liquids~~, ~~hotter locations are Very best Compact Cooler For The Income significantly less dense than cooler places~~.<br>~~<br>Water Provide - In~~ the ~~event that your new fridge~~ has ~~an ice creator or drinking water provide give then there necessities~~ to be a ~~water association made to your pipes~~. ~~The smallest wine coolers hold~~ in ~~between eight and 12 bottles~~ of ~~wine. When choosing a size~~, ~~bear~~ in ~~mind you will will need to leave a compact amount~~ of ~~space to let~~ the ~~wine cooler to vent~~ the ~~heat it creates~~. ~~We'll come to your help with this guide~~ of the ~~best CPU Coolers for your income~~.<br><br>~~Ice cream~~, ~~popsicles~~, ~~even some drugs and batteries require~~ a ~~space in the freezer to keep their consistency and maximum freshness time~~. ~~Apparently~~, ~~wine coolers do not chill wines down to a temperature that one would want to serve white wines at~~. ~~They only cool to 54 degrees F~~ (~~this is the regular temperature British ales were served at~~ and ~~described as "warm beer".~~		In [[algebraic geometry]], the '''Mumford–Tate group''' (or '''Hodge group''') ''MT''(''F'') constructed from a [[Hodge structure]] ''F'' is a certain [[algebraic group]] ''G''. When ''F'' is given by a [[rational representation]] of an [[algebraic torus]], the definition of ''G'' is as the [[Zariski closure]] of the image in the representation of the [[circle group]], over the [[rational numbers]]. {{harvs\|txt\|authorlink=David Mumford\|last=Mumford\|year=1966}} introduced Mumford–Tate groups over the complex numbers under the name of Hodge groups. {{harvtxt\|Serre\|1967}} introduced the ''p''-adic analogue of Mumford's construction for [[Hodge–Tate module]]s, using the work of {{harvs\|txt\|last=Tate\|authorlink=John Tate\|year=1967}} on [[p-divisible group]]s, and named them Mumford–Tate groups.

			==Formulation==
			The algebraic torus ''T'' used to describe Hodge structures has a concrete matrix representation, as the 2×2 invertible matrices of the shape that is given by the action of ''a''+''bi'' on the basis {1,''i''} of the complex numbers '''C''' over '''R''':

			:<math>\begin{bmatrix} a & b \\ -b & a \end{bmatrix}.
			</math>

			The circle group inside this group of matrices is the [[unitary group]] ''U''(1).

			Hodge structures arising in geometry, for example on the [[cohomology group]]s of [[Kähler manifold]]s, have a [[lattice (group theory)\|lattice]] consisting of the integral cohomology classes. Not quite so much is needed for the definition of the Mumford–Tate group, but it does assume that the vector space ''V'' underlying the Hodge structure has a given rational structure, i.e. is given over the rational numbers ''Q''. For the purposes of the theory the complex vector space ''V''<sub>''C''</sub>, obtained by extending the scalars of ''V'' from ''Q'' to ''C'', is used.

			The weight ''k'' of the Hodge structure describes the action of the diagonal matrices of ''T'', and ''V'' is supposed therefore to be homogeneous of weight ''k'', under that action. Under the action of the full group ''V''<sub>''C''</sub> breaks up into subspaces ''V''<sup>''pq''</sup>, complex conjugate in pairs under switching ''p'' and ''q''. Thinking of the matrix in terms of the complex number λ it represents, ''V''<sup>''pq''</sup> has the action of λ by the ''p''th power and of the complex conjugate of λ by the ''q''th power. Here necessarily

			:''p'' + ''q'' = ''k''.

			In more abstract terms, the torus ''T'' underlying the matrix group is the [[Weil restriction]] of the [[multiplicative group]] ''GL''(1), from the complex field to the real field, an algebraic torus whose character group consists of the two homomorphisms to ''GL''(1), interchanged by complex conjugation.

			Once formulated in this fashion, the rational representation ρ of ''T'' on ''V'' setting up the Hodge structure ''F'' determines the image ρ(''U''(1)) in ''GL''(''V''<sub>''C''</sub>); and ''MT''(''F'') is by definition the Zariski closure, for the ''Q''-Zariski topology on ''GL''(''V''), of this image.<ref>http://www.math.columbia.edu/~thaddeus/seattle/voisin.pdf, pp. 7–9.</ref>

			==Mumford–Tate conjecture==

			The original context for the formulation of the group in question was the question of the [[Galois representation]] on the [[Tate module]] of an [[abelian variety]] ''A''. Conjecturally, the image of such a Galois representation, which is an [[l-adic]] Lie group for a given prime number ''l'', is determined by the corresponding Mumford–Tate group ''G'' (coming from the Hodge structure on ''H''<sup>1</sup>(''A'')), to the extent that knowledge of ''G'' determines the [[Lie algebra]] of the Galois image. This conjecture is known only in particular cases.<ref>http://math.berkeley.edu/~ribet/Articles/mg.pdf, survey by [[Ken Ribet]].</ref> Through generalisations of this conjecture, the Mumford–Tate group has been connected to the [[motivic Galois group]], and, for example, the general issue of extending the [[Sato–Tate conjecture]] (now a theorem).

			==Period conjecture==

			A related conjecture on abelian varieties states that the [[period matrix]] of ''A'' over number field has [[transcendence degree]], in the sense of the field generated by its entries, predicted by the dimension of its Mumford–Tate group, as in the previous section. Work of [[Pierre Deligne]] has shown that the dimension bounds the transcendence degree; so that the Mumford–Tate group catches sufficiently many algebraic relations between the periods. This is a special case of the full Grothendieck period conjecture.<ref>http://math.cts.nthu.edu.tw/Mathematics/preprints/prep2005-6-002.pdf, p. 3.</ref><ref>http://arxiv.org/abs/0805.2569v1, p. 7.</ref>

			==Notes==
			{{reflist}}

			==References==

			*{{Citation \| last1=Mumford \| first1=David \| author1-link=David Mumford \| title=Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) \| publisher=[[American Mathematical Society]] \| location=Providence, R.I. \| id={{MR\|0206003}} \| year=1966 \| chapter=Families of abelian varieties \| pages=347–351}}
			*{{Citation \| last1=Serre \| first1=Jean-Pierre \| author1-link=Jean-Pierre Serre \| editor1-last=Springer \| editor1-first=Tonny A. \| title=Proceedings of a Conference on Local Fields (Driebergen, 1966) \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| isbn=978-3-540-03953-2 \| id={{MR\|0242839}} \| year=1967 \| chapter=Sur les groupes de Galois attachés aux groupes p-divisibles \| pages=118–131}}
			*{{Citation \| last1=Tate \| first1=John T. \| editor1-last=Springer \| editor1-first=Tonny A. \| title=Proc. Conf. Local Fields( Driebergen, 1966) \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| mr=0231827 \| year=1967 \| chapter=p-divisible groups.}}

			==External links==
			*[http://www.math.umass.edu/~hacking/agnes/griffiths.pdf Lecture slides (PDF)] by [[Phillip Griffiths]]
			*[http://www.cms.zju.edu.cn/UploadFiles/AttachFiles/2005730145725232.pdf ''Mumford-Tate groups, families of Calabi-Yau varieties and analogue André-Oort problems I'', preprint (PDF)]

			{{DEFAULTSORT:Mumford-Tate group}}
			[[Category:Hodge theory]]
			[[Category:Algebraic groups]]

80.39.127.14: Added reference to Wolfram Math World (Xavi Aznar)

2011-09-01T07:53:32Z

Added reference to Wolfram Math World (Xavi Aznar)

New page

Most evaporated coolers have a tendency to be relatively heavy and slightly bulky which can make them tough to carry about from room to room. The contenders have been a soft-side model from Kelty, the affordable and hugely portable Folding Cooler (58 quarts, $45.95) a pricey pro-level” icebox from Yeti, the Tundra 45 model (45 quarts, $329) and a enormous tank made by Igloo, the Yukon 70 (70 quarts, $389.99), which touts Keeps Cold For 7 Days” right on its lid. In the August heat no cooler lasted for additional than 4 days. We stocked 10 pounds of ice in each and every and let the sun and hot air do its worst. Coleman Xtreme or Ultimate Xtreme coolers — that's what we utilised and block ice lasted 7 days in 90+ degree heat (and the cooler sat in a parked vehicle significantly of the time, so it was even hotter), despite the fact that I did pile blankets and tarps more than the cooler and kept a separate cooler for drinks. Igloo Maxcold coolers — the Maxcold” name has some smaller sized coolers, soft-sided coolers and ones without insulated tops that are NOT what you need. Does not incorporate a CPU Cooler. No ice necessary to preserve meals and snacks at the fantastic temperature, so you can have a lot more area for actual food and drink. With a lengthy road trip ahead, no matter whether you have got small ones with you or not, auto coolers can make points significantly easier. When we reviewed the Hyper 212 Evo in our January 2012 problem, we had two important complaints about it: The backplate mounting procedure remained annoying, and the cooler did not have LGA2011 mounting assistance. When you have almost any questions about wherever and tips on how to work with [http://www.bestcoolerreviewshq.com/best-cooler-for-the-money/ Www.bestcoolerreviewshq.Com], you can e mail us at the website. In order to differentiate in between lower-finish and larger-end models, Igloo and Coleman What Is The Greatest Cooler For The Revenue (among other folks) have adopted a technique of naming and advertising their coolers following the length of time they can hold some thing cold. It relies on draining and weighing the quantity of meltwater made at regular measurement told us the percentage of ice that had melted up to that point in time. In liquids, hotter locations are Very best Compact Cooler For The Income significantly less dense than cooler places. Water Provide - In the event that your new fridge has an ice creator or drinking water provide give then there necessities to be a water association made to your pipes. The smallest wine coolers hold in between eight and 12 bottles of wine. When choosing a size, bear in mind you will will need to leave a compact amount of space to let the wine cooler to vent the heat it creates. We'll come to your help with this guide of the best CPU Coolers for your income. Ice cream, popsicles, even some drugs and batteries require a space in the freezer to keep their consistency and maximum freshness time. Apparently, wine coolers do not chill wines down to a temperature that one would want to serve white wines at. They only cool to 54 degrees F (this is the regular temperature British ales were served at and described as "warm beer".

Einstein function - Revision history

en>Yobot: Tagging + other fixes, added orphan tag using AWB (10392)

en>BattyBot: removed Template:Multiple issues & general fixes using AWB (8686)

80.39.127.14: Added reference to Wolfram Math World (Xavi Aznar)