FL Tariq 㱺 - math.huji.ac.il
Transcript of FL Tariq 㱺 - math.huji.ac.il
AFL for CA paints- -
-
Mcmullan-
HannityFL'-- AFL
'
GGP-Tariq.
-
,
I, f,_⇒ que oftener
,
/ I 1 K¥, ↳ GheeWafd.IM - B
' pushed'm 's
cutin. periods
cycle )
\
Cross . Zggier & Waldspnrga tombs--
Klee ' ing . quadratic
IT = rap , of 9=4 Lz CA ) attached toa
wt.
2 new fanCaspi old
BAT, K ) - { quaternion algebra , BIA at. Bo = HI }
& o ka Cs IB over A
• IT should admit - fl to a rep, 74,3 of B"
(Gael condita.)
B - B"
L,B -
B"
= coherent B ie .IB = B ⑦ A F ! Bho
,Q
B-
= incoherent 1B i. e . a dog wt hold
{ (B) she r ) =+ I ⇐ IBE Bt
.
✓ t ft, Bu guts- I Bu has .li'T
Loghry.
: H ( x,
K,B) = Hay Tpg , c) to for T ! B c- B
.
D B c. B"
,Be :B IA
.
L ( TIK,
s ) = L (Yi 's, Tik )-
Lil,IT, ad )
pick this B,
then
Weldspurge . : PT : KB → C T = #
×
- -Qt
¢ he ✓ OCH de Gig = PB"
( T )
( PT (9) I'
= { ( The,o) - Cece Terms )
to
2) whet about 1B EB ? ee. 113=14265 ) ⑦ HI
O
re Tower f Shinra curves XulqI
X (e) = tf - PBO '
ufaypsfuc.PH?sQ-UpBfs#U
Tforrr.
when th,
Blu ) = the quaternion algebra Iqsit
. Bcuz E Bw iff w # u.
It lbw if u - u.
⇐ Bol- I - Mak )rink
Kya ↳ B → ( YI E LIK,
t ]u e Div ( Xpgu )to CT ]
Chee, de (Yuli = Hut - deglllullkx ) e
Div- HB,u% =
JIB, a-
ICT )ulAH ( tips
,u )
Moduli interpretation if B - IBO-
Xu -
- l E ell . curves, ai TE of IT cell ± ⑦ K
-K E
Ul Kaa Bo
Yu = 4 E hea Cn by K , x :TEA -70,79 } =
* T
⑦ 443,4 )'
4T Un Kh"
Tchler-sh.in"
: JIB,u~ ⑦ AMB-
f-d. V is . (QU
1-(cake ( PIB") Ve Aq,
← IT www.lezwes
'B ' Bo ④ on all Apg st. JL( IB ) = automorphic,it
.2
up . of GAA ) .9. B. a-
X. IN
fee. µ. c- ftp.iy-
I
QQA
k tf . . f. I e 5. Crowl )"
"B Els
Ef.
PT : tiple → A CK ) PIB'"
"
y- g. ( YI = ! , ycfie.tl)
' t
q- c - I
Hegner pt.
Them (Gro . . - E -j.us?-heng,Yu-n?'7hay.wI-huy)pick 1B as punt, Val cerithium
, assume ECB ) = - iFA
u
ECITK,
'
k )
( Ptfe ) , Rely L' (The.
o) - (bad term )G. y - 1
If Rauf TY, (KY are disjt, can Take y = new vector ,J ⇒ = ,
(, 7W , : ACK ) ⑨ A' CK ) → "2 AI
,,= Aq;
A = ( y' = X3t - + → b l J P = ( x : y : . ) x -- tf r -drug
( P, PSN , = leg (wax Ipl , 191 I + 011 )
RTFappquits This
• ( Paty) , Palle' )) = ( ( 470
, y't
y ; ( YT >A JIB
, a
= ( ( 410 , 147. HB) > first #Bt-
= (fro )
J (fB )= ( (YT , l 'll'
- THB ) ) = E JaffasTiz 1B
-
• I ( f. s )-
- RT're," ,,
⑦ pen.gg ..
) - E Us) Na-
Y' Hk
A- f. dasTT'll 's) "
*Ig , ¥,
9/4/91 'd Nfl-4149161/4%6
= L (The,
s) . Tf Ia, If.ir )
Geometric expansion-
orb ( d. f. s )Ifla'd b)go,
f r. . .I It
,
ol ' I AHH 'langue.
Je. C.rsat IA db
= To .br/dit.s).
U
Read bed Transfer :
• baleful orbit, *"
la = ¥,first, F -
- eat lgbg!
Efc ! ) →I Linus B - K Kj
delta E F- ton),
cry,#t - at Pj
• take Aneta ,
f- ← Lip.
⇐ orb. ( d. f , =/
°"B ! if raga B
O else .It
¥ , fpfti'
rt . ) did .
Supper ther B i , incoherent, I ← fry
orya.← r c- §Bf, B coherent
.
th,Bu ¥ Bu
,Orlov ( S , f. o) - o
• since I at leat one Shehu,⇒ Orb ( d , f. o ) - o
⇒ Orb-
( d. f,o) - § Orb
-
( d,f. ol - Orb:( dif , o)
⑨ Moreover,
this is zero if Bu # Bu et wore thineruv
.
° so if nonzero,
B -- Blu )
since K as B"
↳ B!This wit happen if u split, in K
Cardin : I'
tho ) i § g¥↳,,0- b f. o) . Orb:(d. Lol
hasplit-
in K H
orbulr.fas.co) .
• feanetiic expansion of Jf-
Jffps ) - C l 'll'
. WITH D= ⇐ ( Cmo, CYY TUBB.
where , if u is a fist . place of good red. for X ( Uu --marine
'et I -- integral mail , y
,
43,u
Bu split )
( Edit,ECQ;D: me
,#E. Et pf# X'
egoeii, a#t tauto fr CK )
Assume . X - modeler cum ( BIMINI )
← fort IYT us . ly )
•
pinert in K
caplets'm of• extend sales to Ote
, p= I = max 't wer- tied
out of OK,
.
1.
FI .
Fact : if Ez is ell . came w/ CA by K
then redp(Ez ) is ss .
⇐ up nonsplir in K.
Rink : if p splits in K,
then=
( I -2k,
t ),
Lare it - VI),
to
a" is the.
!r
:'
. §. ^Gd
J -
- Eon,". i. K ¥
Tp
↳ X"
- ¥74 ' B''
'''
ya . /T¥ XPBCPY
es ft schaus an Ep OI,
m-
where : Nfs ) . } g - p- du gp/g,
c : f KEG. -99-1 om EF113 ' Bo II
= Spf 75. EUI .
go - thep - dir . group of a Ss . eh ' cure/,pj=k
= thewipm
commendp- dir
go of dyingProd :
thewar
is
⇐ ay - 4S -
- E. imma:{÷!: )Bo \
( bunch on y U
End ( Go) ④ Q- Bcp )
,
T "
Go = (EP)'
GL , fam ) D
Ig ) - Ian,g)
NI =" ( f: " . f." '" ' * "I
e. puas% .PIBCP
= I int , I ITIBCP / X
"
) = z + pipe ' '
Plz,¥ 16 "
=Orb
"-
( 8. LB ) D
-
y M¥43 , learnt .bg , I
trap - tops;
t
'
malt! . him=
mn ( lil . ( t.pl ) E - t.lt,
= ur
II m is mail. c. y
N
re QI. ett. is Antes!%) a
" Su , #tAnt IS . ) m%pm
End (Gp)> ' " s dl 86%10. . . End (God
, ,104 l .
Ok. ..
H 013,1.
H o Gros.' then
, at gun :Ok + P
" ' '
OB,
canid
OB = Or - Ge j lifting .
✓ = atBj p.ae Ok,ae0E o F. ketone 's talk
tj=j to K
ueljl '- i.
inv ( at pj ) - 2nd Ip) - i
Tit inv ( - I
m =
# .
11
ATL m ( al . 483) = orb'
!! ,o ) .
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