h&. AUTOMORPH 1SM AND GAL01S THEDRY
AukOmoaphitm i e fields
ld
envesovn qa ield f , Two aleen
be a algehaMC
, E oN
a
co are
Co ov
F Sald,F) -aa Cp P),
H.E
Ami i»aaduib. polgnomi
a 3 epes L
ie
F
ov
with
hesblu poynomal
ad-aL 3 xoes 5R3ad
eve
K,
iLdutible Rl aad a coogae
a-2
adutöbla polypoma
2,J2 3 eaots
Longahs ove .
whch is
Saadncsula in d a
Thoaun the Cosaahon Jsomoxroiso F
tva
ad B e algebic
a field, od ut
Letf be
4 P . F x ) F ( E ) dad
lh dag (d, F) n . 1he map
M
+Cp-
e CCoC* Cn-1
Fl) oob FCP) 6 a
costP is an isomorphi3m
oVe F
Suppoye that , F C )>PF) deimd
ba
M
Cn +CF ** f af
,t t +--.
, Is an io wmD Lphsm aCP,P).
iAA FL dides h p,F).
pegneiial mono 2 *iF iaa (p,
CeC« * wa
hon
ovea P
a0 tooa
ofaar
Shave So
So
Coveaia
: is a)
isomesph, Supppse ha,
evaluaHou
3AA
Ct7 ) *
hen me Hon
ie s aLio a
3eO (d, F). Ah. , F)
f an oom2sr : Flx) Fl0 md FJ-f
he Hhcosem het e be an tnhmon ield o
F, hen ut m
& awe he scma kam <pin
AEE, wnt d i algebRDAC Ovea
JARdCbll poljnoial pen) F[) s ueh Hha pld) :0. fundamansl mom ok omomephisr
daheiw na4
T isad utbble plyomal pta) y un ianebo
tple c nsaor fac 'o m F md y a pohyom*
miun a dg kee z) in Fl) hav d s a 3eso
:F tCFL)-FU)
fta)0 for fea) EFl) ailb fca) fo, han pen)
dvids fen) Coupond»g to a n isoipis,
ms imphes Hhak, Ma iAa(p,F) dids 33a(a F), p Flec) FCF)
Sinslas
de ve, p algebraic ve F uan Rmedmcska her
an
As e CoroposshoM otutO tsomoaph
Smu w ww.onphiro wch nus fo F ) to FC).
, i ' s an o moaphsnm
Now Con $elea
F ()
.
t Cio+ . .+(, .
AukOmoaphitm i e fields
ld
envesovn qa ield f , Two aleen
be a algehaMC
, E oN
a
co are
Co ov
F Sald,F) -aa Cp P),
H.E
Ami i»aaduib. polgnomi
a 3 epes L
ie
F
ov
with
hesblu poynomal
ad-aL 3 xoes 5R3ad
eve
K,
iLdutible Rl aad a coogae
a-2
adutöbla polypoma
2,J2 3 eaots
Longahs ove .
whch is
Saadncsula in d a
Thoaun the Cosaahon Jsomoxroiso F
tva
ad B e algebic
a field, od ut
Letf be
4 P . F x ) F ( E ) dad
lh dag (d, F) n . 1he map
M
+Cp-
e CCoC* Cn-1
Fl) oob FCP) 6 a
costP is an isomorphi3m
oVe F
Suppoye that , F C )>PF) deimd
ba
M
Cn +CF ** f af
,t t +--.
, Is an io wmD Lphsm aCP,P).
iAA FL dides h p,F).
pegneiial mono 2 *iF iaa (p,
CeC« * wa
hon
ovea P
a0 tooa
ofaar
Shave So
So
Coveaia
: is a)
isomesph, Supppse ha,
evaluaHou
3AA
Ct7 ) *
hen me Hon
ie s aLio a
3eO (d, F). Ah. , F)
f an oom2sr : Flx) Fl0 md FJ-f
he Hhcosem het e be an tnhmon ield o
F, hen ut m
& awe he scma kam <pin
AEE, wnt d i algebRDAC Ovea
JARdCbll poljnoial pen) F[) s ueh Hha pld) :0. fundamansl mom ok omomephisr
daheiw na4
T isad utbble plyomal pta) y un ianebo
tple c nsaor fac 'o m F md y a pohyom*
miun a dg kee z) in Fl) hav d s a 3eso
:F tCFL)-FU)
fta)0 for fea) EFl) ailb fca) fo, han pen)
dvids fen) Coupond»g to a n isoipis,
ms imphes Hhak, Ma iAa(p,F) dids 33a(a F), p Flec) FCF)
Sinslas
de ve, p algebraic ve F uan Rmedmcska her
an
As e CoroposshoM otutO tsomoaph
Smu w ww.onphiro wch nus fo F ) to FC).
, i ' s an o moaphsnm
Now Con $elea
F ()
.
t Cio+ . .+(, .
