2 cas - math.columbia.edukhovanov/ma2_fall/files/lect_9.pdfw man usado a(z) f 3() ea anauakl elemt e...

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(iedan & sf dds Rt»n) ech 9 N exers Fe E FCE, J eE. Rave a hmpin ev: Fl^) -E T ev FC] isa suy{E ev f (x)) = 4(2) doma in nc 2 caS njue PeF(=) eP), Pao ^fa #0. )ke a, io}3 oue F Exampe <R Lnev Fla2) ncln d Ta arsan de ade FLA) F() 1 ot a ea 's aa sonenis F) FLA) e E F e Sopisn 0is can F E eve a FLA F () na s F() Froe (Fl a]) eFL F is a Rld e is j chu F ( F()CE w man usado F a(z) 3()

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Page 1: 2 caS - math.columbia.edukhovanov/ma2_fall/files/lect_9.pdfw man usado a(z) F 3() Ea anauakl elemt e E atca dakl 0-e F onaaes a ary Fh) , IS ta Aunakons oe f, i E aes Fe FC)

(iedan & sf dds Rt»n) ech 9 N

exers Fe E

FCE, J eE. Rave a hmpin ev: Fl^) -E

T ev FC] isa suy{E ev f (x)) = 4(2)

doma in nc

2 caS

njue PeF(=) eP), Pao ^fa #0. )ke a, io}3 oue F Exampe <R

Lnev Fla2) ncln d Ta

arsan de ade

FLA) F() 1

ot a ea 's aa

sonenis

F) FLA) e E

F e Sopisn 0is can

F E eve a FLA

F () na s F() Froe (Fl a])

eFL F is a Rld e is j chu F ( F()CE

w man usado

F a(z) 3()

Page 2: 2 caS - math.columbia.edukhovanov/ma2_fall/files/lect_9.pdfw man usado a(z) F 3() Ea anauakl elemt e E atca dakl 0-e F onaaes a ary Fh) , IS ta Aunakons oe f, i E aes Fe FC)

Ea anauakl elemt e E atca dakl 0-e F

onaaes a ary Fh) , IS ta Aunakons oe f, i E aes

Fe FC) <F( J) CE

inTdu massne0-en F

alpoar ada E

F) F() hasis,d', ..

3 2) ke e 4 [o). a yonlPeffx), Pa)-o

ialgaalc oven F.

Peepoibo e FCE SS exrtenSron, de sa'e ow F.

Tan ker - p), eF]an ireduciba pnon2.

eFCa), ?u)= ple iSo me isn F(z)ȣ I duus

év. (a+ (e)) = L. FL]-lm ev, is kAk

V e is o idaa, ncpo.

B s SoOlkonun set i d isan's

Flx/ e Fl) , F[4)F(x) e 20 FC a doah

F r lama

e max idud S e a pr,

a e ) peP) cdu

Ga)-

Page 3: 2 caS - math.columbia.edukhovanov/ma2_fall/files/lect_9.pdfw man usado a(z) F 3() Ea anauakl elemt e E atca dakl 0-e F onaaes a ary Fh) , IS ta Aunakons oe f, i E aes Fe FC)

PCE

-3-

F= FC).

F(L) a t aas boh Fea

sre" aa F, n ulabon ista nscanda. l Fc FL4) cF(L)CE

FeE,

ege ARd, rado

)

is aalraie Fc F(J-F() CCE FcF

Can chao x ode

P ir (4, F)

4,,*

isa a sts AL FA)

CF:P=a Sa

ta-, Roe sd ean

din E

lemma (Riedmor, anma l.4)

FeE orsun kdJ, se F. "prox P eFC*] is a eu

vode Pelyoni s.t. pa\o. Tun p=ise (a, F).

ra x-2- ic (2,@).

onic, reduci, p(G)= 2-2 =o

ire a (E)) = z-

ir (2, & )=x-2 s i, sn 2 rabsn Q() 1rc (, q(ra)) = *23a irr (6, a)

exen

Page 4: 2 caS - math.columbia.edukhovanov/ma2_fall/files/lect_9.pdfw man usado a(z) F 3() Ea anauakl elemt e E atca dakl 0-e F onaaes a ary Fh) , IS ta Aunakons oe f, i E aes Fe FC)

49) Pp (ura ula, tman lemma 43) FcB cE

CF F] LE:8)CR: F).

P S4 a hants F/B, } sis 5/F.

) S spans . yeE ,

-2 C PsA*

2 au i da, AsSu ohm

2Cs ; 4*o Br s C eF

Page 5: 2 caS - math.columbia.edukhovanov/ma2_fall/files/lect_9.pdfw man usado a(z) F 3() Ea anauakl elemt e E atca dakl 0-e F onaaes a ary Fh) , IS ta Aunakons oe f, i E aes Fe FC)

Exaup (Ratman,

V3 ode an (, Q)= 3 B srake on B. (

(,8)|3 Ce: Q(6))= 2 ,sms 4 QEI

f a blz a,s a3aa* 2a>W2 t 26 > Sina is raho

t. (6.6)>afG sa 2

-10 +2S- 24 wllslo Sao a polno m

Qc()e F, (,Q) s du . EQ ()

Atanatue: CL 2G+ 2 eQ( +,36+ 23 ¬Q()

QA= (G,6). => ir(:,a) has á^u 4,as skimd

Page 6: 2 caS - math.columbia.edukhovanov/ma2_fall/files/lect_9.pdfw man usado a(z) F 3() Ea anauakl elemt e E atca dakl 0-e F onaaes a ary Fh) , IS ta Aunakons oe f, i E aes Fe FC)

2 een

3 4 G 4

(O (O S da. 7 7 W

IS 20 IS

7 3S 3S 21 2 W Ww

w ww

10 2 8 2 8 G

36 4 12G 26 34 36

(aab)P= a . L" (omu)

()= waP ,2,.. P P

R pR

6m mua hue u (a *uy=a-LtR

7 (a) sa p i tm RR 3p RR

(t~oo

Exous F isa ife eld fro be us enomorplasn Ff

sh ckue (Gn aus oiSa ).