[permalink] [id link]

If f is unramified at a point x, then f is quasi-finite at x. Conversely, if f is quasi-finite at x, and if also, the local ring of x in the fiber f < sup >− 1 </ sup >( f ( x )), is a field and a finite separable extension of κ ( f ( x )), then f is unramified at x .< ref > EGA IV < sub > 4 </ sub >, Théorème 17. 4. 1 .</ ref >

from
Wikipedia

## Some Related Sentences

If and f

__If__F

**is**an antiderivative

**of**

__f__

**,**

**and**

**the**function

__f__

**is**defined on some interval

**,**

**then**every other antiderivative G

**of**

__f__differs from F by

**a**constant: there exists

**a**number C such that G

**(**

**x**) = F

**(**

**x**) + C for all

**x**

**.**

__If__we define

**the**function

__f__

**(**n ) = A

**(**n

**,**n ), which increases both m

**and**n

**at**

**the**same time

**,**we have

**a**function

**of**one variable that dwarfs every primitive recursive function

**,**including very fast-growing functions such as

**the**exponential function

**,**

**the**factorial function

**,**multi-and superfactorial functions

**,**

**and**even functions defined using Knuth's up-arrow notation

**(**except when

**the**indexed up-arrow

**is**used ).

The tensor product X ⊗ Y from X

**and**Y**is****a**K-vector space Z with**a**bilinear function T: X × Y → Z which has**the**following universal property:__If__T ′: X × Y → Z ′**is**any bilinear function into**a**K-vector space Z ′,**then**only one linear function__f__: Z → Z ′ with exists**.**__If__

__f__

**is**

**also**surjective

**and**therefore bijective

**(**since

__f__

**is**already defined to be injective ),

**then**S

**is**called countably infinite

**.**

__If__we attempt to use

**the**above formula to compute

**the**derivative

**of**

__f__

**at**zero

**,**

**then**we must evaluate

**1**/ g ′(

__f__

**(**0 )).

__If__

**the**function

__f__

**is**not linear

**(**i

**.**e

**.**its graph

**is**not

**a**straight line ), however

**,**

**then**

**the**change

**in**y divided by

**the**change

**in**

**x**varies: differentiation

**is**

**a**method to find an exact value for this rate

**of**change

**at**any given value

**of**

**x**

**.**

__If__

__f__

**is**

**a**continuous function

**,**meaning that its graph

**is**an unbroken curve with no gaps

**,**

**then**Q

**is**

**a**continuous function away from

**.**

__If__

**the**limit exists

**,**meaning that there

**is**

**a**way

**of**choosing

**a**value for Q

**(**0 ) that makes

**the**graph

**of**Q

**a**continuous function

**,**

**then**

**the**function

__f__

**is**differentiable

**at**

**a**

**,**

**and**its derivative

**at**

**a**equals Q

**(**0 ).

__If__

**in**

**the**third identity we take H = G

**,**we get that

**the**set

**of**commutators

**is**stable under any endomorphism

**of**G

**.**This

**is**

**in**fact

**a**generalization

**of**

**the**second identity

**,**since we can take

__f__to be

**the**conjugation automorphism

**.**

__If__m

**and**n are natural numbers

**and**

__f__

**(**

**x**)

**is**

**a**smooth

**(**meaning: sufficiently often differentiable ) function defined for all real numbers

**x**

**in**

**the**interval

**,**

**then**

**the**integral

If and is

__If__his dancers are sometimes made to look as

**if**they might be creatures from Mars

**,**this

__is__consistent with his intention

**of**placing them

**in**

**the**orbit

**of**another world

**,**

**a**world

**in**which they are freed

**of**their pedestrian identities

**.**

__If__

**a**work

__is__divided into several large segments

**,**

**a**last-minute drawing

**of**random numbers may determine

**the**order

**of**

**the**segments for any particular performance

**.**

__If__Wilhelm Reich

__is__

**the**Moses who has led them out

**of**

**the**Egypt

**of**sexual slavery

**,**Dylan Thomas

__is__

**the**poet who offers them

**the**Dionysian dialectic

**of**justification for their indulgence

**in**liquor

**,**marijuana

**,**sex

**,**

**and**jazz

**.**

__If__he

__is__

**the**child

**of**nothingness

**,**

**if**he

__is__

**the**predestined victim

**of**an age

**of**atomic wars

**,**

**then**he will consult only his own organic needs

**and**go beyond good

**and**evil

**.**

__If__he thus achieves

**a**lyrical

**,**dreamlike

**,**drugged intensity

**,**he pays

**the**price for his indulgence by producing work -- Allen Ginsberg's `` Howl ''

__is__

**a**striking example

**of**this tendency -- that

__is__disoriented

**,**Dionysian but without depth

**and**without Apollonian control

**.**

__If__love reflects

**the**nature

**of**man

**,**as Ortega Y Gasset believes

**,**

**if**

**the**person

**in**love betrays decisively what he

__is__by his behavior

**in**love

**,**

**then**

**the**writers

**of**

**the**beat generation are creating

**a**new literary genre

**.**

__If__

**the**existent form

__is__to be retained new factors that reinforce it must be introduced into

**the**situation

**.**

__If__we remove ourselves for

**a**moment from our time

**and**our infatuation with mental disease

**,**isn't there something absurd about

**a**hero

**in**

**a**novel who

__is__defeated by his infantile neurosis??

__If__many

**of**

**the**characters

**in**contemporary novels appear to be

**the**bloodless relations

**of**characters

**in**

**a**case history it

__is__because

**the**novelist

__is__often forgetful today that those things that we call character manifest themselves

**in**surface behavior

**,**that

**the**ego

__is__still

**the**executive agency

**of**personality

**,**

**and**that all we know

**of**personality must be discerned through

**the**ego

**.**

__If__our sincerity

__is__granted

**,**

**and**it

__is__granted

**,**

**the**discrepancy can only be explained by

**the**fact that we have come to believe hearsay

**and**legend about ourselves

**in**preference to an understanding gained by earnest self-examination

**.**

If and unramified

__If__we say that

**is**formally

__unramified__

**and**

**if**

**is**

**also**

**of**locally

**finite**presentation we say that

**is**

__unramified__Vakil's notes

**.**

__If__Φ

**is**

**a**prime

**of**L lying over φ

**,**that L / K

**is**

__unramified__means by definition that

**the**integers

**of**L modulo Φ

**,**

**the**residue

**field**

**of**L

**,**will be

**a**

**finite**

**field**

**of**order q

**<**

**sup**

**>**

**f**

**</**

**sup**

**>**extending

**the**residue

**field**

**of**K where

**f**

**is**

**the**degree

**of**L / K

**.**

The multiplicity e

**(**j ) are called ramification indices**of****the****extension****at**p**.**__If__they are all equal to**1****and****if****in**addition**the****field**extensions B / P**<****sub****>**j**</****sub****>**over A / p**is****separable****,****the****field****extension**L / K**is**called__unramified__**at**p**.**__If__

**is**

__unramified__

**in**L

**,**

**then**

**the**decomposition group

**is**canonically isomorphic to

**the**Galois group

**of**

**the**

**extension**

**of**residue fields over

**.**

If and at

__If__I even hint

__at__it do you think it will matter that you are his nephew --

**and**not even

**a**blood nephew ''??

__If__you tell him I made

**a**pass

__at__you he might think you misunderstood something I said or did

**,**so instead

**of**just telling him I made

**a**pass

**,**say I tried to date you

**and**that you agreed so you could prove to him what

**a**louse I really am

**.**

__If__

**in**any one calculation Ptolemy had had to invoke 83 epicycles all

__at__once

**,**while Copernicus never required more than one third this number

**,**

**then**

**(**

**in**

**the**sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican

**.**

__If__nothing else

**,**

__at__least two good songs came out

**of**

**the**project

**,**`` Out Of This World ''

**and**`` June Comes Around Every Year ''

**.**

__If__his scholarship

**and**formal musicianship were not all they might have been

**,**Mercer demonstrated

__at__an early age that he was gifted with

**a**remarkable ear for rhythm

**and**dialect

**.**

__If__

**the**hardships

**of**

**the**winter

__at__Valley Forge were trying for healthy men

**,**they were

**,**

**of**course

**,**much more so for those not

**in**good health

**.**

__If__it proclaims that

**the**best

**is**yet to be

**,**it always arouses

**,**

__at__least

**in**

**the**young

**,**either

**a**suspicious question or perhaps

**the**exclamation

**of**

**the**Negro youth who saw on

**a**tombstone

**the**inscription

**,**`` I am not dead but sleeping ''

**.**

__If__

**a**broader Atlantic community

**is**to be formed --

**and**my own judgment

**is**that it lies within

**the**realm

**of**both our needs

**and**our capacity --

**a**ready nucleus

**of**machinery

**is**

__at__hand

**in**

**the**NATO alliance

**.**

__If__you're lyin' out

**in**

**the**hammock

__at__night

**,**

**and**it gets kinda cool -- you know -- you just take these sides with

**the**fringe on -- see --

**and**wrap 'em right over you

**.**

Mr. Richard Preston

**,**executive director**of****the**New Hampshire State Planning**and**Development Commission**,****in**his remarks to**the**Governors Conference on Industrial Development__at__Providence on October 8**,**1960**,**warned against**the**fallacy**of**attempting to attract industry solely to reduce**the**tax rate or to underwrite municipal services such as schools when he said: ``__If__this**is****the**fundamental reason for**a**community's interest or**if**this**is****the**basic approach**,**success**if**any will be difficult to obtain ''**.**__If__he were to go with White

**,**he would be out there two days

**,**not just listening

**in**

**the**dark

__at__some

**point**between here

**and**Papa-san

**,**but moving ever deeper into enemy land -- behind Papa-san -- itself

**.**

__If__he had any worries

**,**it was only

**the**small ones

**,**about Mother

**in**New York

**,**

**and**his daughter Edwina

**and**what she might be doing

__at__this hour

**,**with her Aunt Asia

**,**

**in**Philadelphia

**.**

__If__we sit here reading editorials

**and**looking

__at__public-opinion polls

**and**other reports that cross our desks

**,**we should realize that this

**is**raw

**,**undigested opinion expressed

**in**

**the**absence

**of**leadership

**.**

__If__our national interest lies

**in**being able to fight

**and**win

**a**war rather than committing national suicide

**,**

**then**we must take

**a**much more penetrating look

__at__ballistic missiles

**.**

__If__our SAC bombers were

**,**today

**,**capable

**of**surviving

**a**surprise missile attack

**and**because

**of**infinite dispersion or long endurance had

**the**capability to strike

__at__Russia again

**,**

**and**again

**,**

**and**again

**,**those bombers would unquestionably assure our military dominance

**.**

__If__your state has no provisions for

**the**numbering

**of**pleasure boats

**,**you must apply for

**a**number from

**the**U.S. Coast Guard for any kind

**of**boat with mechanical propulsion rated

__at__more than 10 horsepower before it can be used on Federal waterways

**.**

__If__

**the**lever

**is**pulled to clear

**a**signal or move

**a**switch

**,**

**the**tappet moves

**a**short distance lengthwise

__at__

**the**same time

**.**

__If__

**the**background

**of**design

**is**too smooth

**,**or you wish to create

**a**wood-grained effect

**,**it may be added

__at__this time with

**a**dull tool such as

**the**handle

**of**

**a**fine paintbrush

**.**

0.139 seconds.