2nd
kyolo-HefeiworkshoponArithmet.ieGeometry
- Higher residaepaimgforpojed.ieSmooth Complete interaction
.
JohnRk( Post.ch )Aug 19 .
2020
1
Higherresidaepaimgforpojedie_smoo.tnComplete interaction.
一一
J이자 with
JaehyunYim.IR"
Train가〕 = I Higher residuepai.mgG.CN
. → Ga) homog.p.ly A qualified version of then
des G씨 = di .in . i k Cup Product .
Colega trick ( C.I.nshypersuf.ae)
소 = a Smooth Picture isRG) IN A its.in.is
Complete interaction Variety . 1 E =Gil) ⑦ 0inde.fmd by G =- Aero r
X- 싸이 두 〖"
(〖"
고 심 T.xoi.is
Ric (田 ) = '조 ( Ch )Canada Him ( X . G ) = :HitThe Cup Product Ric(미에 一叱 ( chart)
k
1H × 1H → H리쎈X,2£ Where S - I Yi Gil E )
E)
2
%, X , ... , N .
Y .,
' ' '
, Yk abdianl.ie ofn S : G → End ( A )
트 = 회 봆 홊和 읺 이 ↳ 퀎쯞Where N = 까마1
.
크
(due)장:
The delay -Easy Complexd ki) = 1 de( Yi) = di A Lie as Lady :
not ki ) = 0 wt ( Yi) = I Allcost
... →sttis미에 一k쎗쏖 Q에
xe isN
ex e actor on IN Q = I 2읇i즚 아서자이와.coi= 1
'
( aw) . ( G,
一一 .
, 용 )
= CN,
一一 .CN,dwy.i.dw.gs
스 = 뾹 즕i큮i ' 바석가에요제
A . S7 .@ - - An
The background charge ciid.in) A.sn.mn . @ [email protected]) AI = He charge export ofEach(S) =o.at(S ) = 1, Sin = He weight w-patof.AE
3
Pie ,
dte) Dies d) Composition of then above G- lineardedei ) - dei)= 0
e-mail ){ 에이에 -에에다maps.CA
0
gN =자사 ,t t.ee?qissurjectieand
也慽.si.co,
샤이온]
ii. K다9 = (QstA )ai ) .
Thuslist횮이..., B - 이온
,이.co,
to와 (ㅿ兪,ai ,一入 卜健妬 .
R사2 ×
老啖 ,대상김미에이
毗八Xs 卜岱熟叭仙 for We have= dB) # Res
. 똔卜帖紘 .es 寸給抵炷: F 成何烘'
)
Let 9 di → 卜健如 be.ie as Evector Space s .
4
Rate G is The contracton operator witht. . wt
씨 씨 (S읎 ,Qs,
ㅿ ) 대→ 詠坰.de D te vector Field 췱 wtlq.iq .즗is a cochamisomorphi.vn .
(4) 〖(E)YS
에 5 : 他胱,
dStd) T (九堈).이
,d ) s ftp.isauaffnebuudle
〖"
(XG나dimensmkl.is
a codainqaasitsomnt.im .
The pr.is a honorary equivalent .(San) ( E e )로 Define
= 세신사서 ( N1시에 !-난조rdq 5년) = (즈,G. 門一的" , ...
, Gil '.si왹s川 tre _
e =lemcd.dkEt Eli diThen SE) is a well defnedsed.in of P도
.
(3) dei) = d(da),
i = 1,2,
" '
.시
wtq) = at ( dei ),i = 1
.2.
"
. 시(5)
peg Bdefdonthetferentdtrmsh.isThe contracton operator withGot any onthecohdogydassesl.tkvector Field 촑시 dlG.iq .즗i ( See Times
,
Laura 12)
5
Ianma 인 saggets The following We
defneacodemmapiquan.tnComplex (薛烋圃燧幽 "! "附岾" (ftp.Q.tk/D-ff.Qs)expansion of ta,Qs )
(寸磯》 , AHA ) with He formalby Taking He quotient by Set
.
parametenks.at#gmgch(h=o ( iesend.mg" k = o "
WHY ) = 1 : te Classical at of The
{WEB) = o Sh(k ) =0 quantl.in Complex )
Note that at(N = -I its thato→siesfei-fp.at(KA) = 0
.GHQst싸가I
'
Theodore WestKA) = o E :
범 : = SidneyCh(QS) = de (Neo also inpl.es that (Q에서 ㅨ※세 )
d (AHA) = 0.
伐川 _ t.tk#m_• (AHA) (s救們
" )(Sit )) , Q.tk/DisaI-fiHeredcomplex: =sina.E_fa.me
묘.
(8HA) (Sir)"' )• _m def設幻'A식스 ) = : (Al꺡 아싸, We also have an exit seq :
o → 卄必 → 昭凸S%aE.isme묘.
6
Pa.
The table Def III다. dnf = : M
( Sick)) , QstkA.lt . ,
• ) )-
-
ifis a shifteddg.la
.TH = then Space of And feet
(difference gradedl.ie algebra) vector Seas on H.
Assame that G = im) t츧.
di = o If We lot {다 : 水一工} thecaordi.ae
( 신 is ColdTau ) ttheaff.ae mauifdd 씨,then
Re The qaadro.pk TH = 씨 杜刀.
a:en , • , a,
안 ) is a DGBY algebra.
人飛 尸者.ci )凡士〗卄仁 卜慌條 Where qoqisassumedt.be ± linearFrom thepreviousdscussion.ae have
a Elinear Born NI :
i'(卄妙 t.INT 버 8G에 B The Jacoban ideal of( a 卜叭 수 theeommddiver.mg di = T.ae
"
non - canonical"
defmedinthelevddef.net쟚쌅띒 of of achains . Gerardd by 쭣
.
,...
,쓨,
.
>
We have an exit sequence of CE는水幼 -modder@0-sQsAieiKhDsS8EtIKkD-sTfm_.oFor each deI,wedef.me a Connection
atn T수퍼때》 -7 제4세
1HE切收》Notation : by Tin = 씼즕 씼
.이)fkttnu.li ⇒ Ta ) 一志iu.tk)
"
= 크 다까고 자사이t T.co
for 꾀 ET버 or ME Side for WE S8任水入》.
fibset ②
dooses.ua : de I3 E f et Tes We also deAre a Connection"
又幷 : 玄收乂 -3玄氏幼리사파m B a as of Half )
by 감사 ( w) = %. 츓," 에Let L- Tiii.
= 즗 (이 t$+4 .co
Using The Bornoption A WE S8任水幼 .
S8ft水幼 These are well -defmedoncohomohyda.es,
T-is(f任水卯 鬼 TH"" Since a Commons with in and 又秒
We dei de Gas -Main Connection"
These are and te Gas_Mannomectm.sn제떼) aer 1시 t
8
DI.
( Higher residuepair.mg)tf T.ee〕 - ut Ims) A higherresiduepaimg.AT,7 : TH X TH -3 £任刀 is a 伍切一bilinearsymmetricpai.mg
Max
7 (Elias) - Ann,
a,Media K :T사세 × 大兆幼 → 杜水卯
[90G(es = T.wsWhere Aa.ie 杜可 is Unique1g ( kcw.ws ''幽唜
.
K'"(w.int#.)determmedby St
.
10 K ( wi,W2) = K (www.T
9M. .de 二工 Aut 락 +& (Rum) ② SK) . kcw.in) = K (SA) .ca
,
W2)5EI = K (We
,(D . W2)
then An.ie c杜刀 G 9k) EFE水幼
Neue e f'
任木③ 지시에 W리) = K( T회.ws + K(wi
,The)
R-t The following diagram Common apt.sn④ 2€K씨에 ) = K(T씸 . .cn) - K(wi
, its )⑤ The Glory diagram Canada :
리드. (K'이
iii] 斤岬幻 → C판阮幼1H × 1시57
~ 11伏箋 → e l n I
Product r
nr
TH X 재-> as
The Higher residaepairig.is an Extensionof The Cup Product of M to He quantitative Where R B a 姃切-linear geometric parent
Coming from He Cup- Product ping of 벗ofones THEN So that if is composite H誌妬 )with The Gas _ Main ConnectionS
.
9
Iowa If Sea : de I3 : Q5basis of-
,쁘) ①
,② : obv.ws by den .
Jaythen A event Def任水幼 ③ Alone fromdietompakhasithaeeostsaunqu.AE任水幻
⑤ : flow from Profte I St.
玉二 촚쎎 랑 ta (삼 )for Some At I'任水叭
.
thn.ttwedefmekieis.ie) Afi
,
A Eli ] = E9 o G ) (WiiI,
i 긔.
2
then K :제4세 ×제4M) → 堈幽)
B thehigherresiduepa.mg .