synthèse de travaux : modules sur l`algèbre de steenrod

K(V, n)

Pp
Upl//Fp,
UpFpFp
Fp
FpFp
pPp
Up
Fp
Up
Up
l
FpUp
Fp
Fp
FpGL(Fn
p)
Fp
Fp
Fp
K
K

PpFp
Fp
Pp
F Pp
Pp
ApFp
FpA2Sqi, i ≥0
∆Sqn= Σa+b=nSqa⊗Sqbp
Apβ P i, i ≥0
Ap
Ap
Up
A2M
Sqix= 0 i > |x|x
Sq0
p
p= 2
x Sq|x|(x) = x2
KpKp→ Up
U:Up→ Kp
XAp
(1)
H∗(X;Fp)Kp
p V
H∗(BZ/2; F2)F2[u]
1F2[u]
p > 2H∗(BZ/p;Fp)
Λ∗(y)⊗Fp[x]
(1)

1 2
Λ∗(y)⊗Fp[x]
βy =x
H∗(BV )H∗(BF)⊗dim V
V7→ H∗(BV )
FpUp
H∗(BV )
UpTV:Up→ Up
H∗(BV )⊗ − :Up→ Up
(2)
(3)
Z/2
Fp
UpFpF2
Fq
Fq
U
(2)
(3)

(4)
Up
Up→
VF?VF?F2p= 2
Z/2p > 2
U2
p2
p
H∗(BZ/p)Z/2
BpA∗
p
pZ/2
B:= F[u]⊗Λ(τi|i≥0) ⊗F[ξj|j≥0] ⊗Λ(w)
B
H∗(BZ/p)
H∗(BZ/p)B
H∗(BZ/p)
wBw
ξ0−u2
p
Z/2Bp////˜
A∗
p:= Bp/hw, ξ0−u2iUp
˜
A∗
p
˜
A∗
p
Up
(4)