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 ) .

-

:

n

aiauco, ( O -E. o)- Y