72
N.M. Katz:
For each Qconjugacy class A of irreducible Crepresentations of G,
the element
(4.4.0.2)
P(A) der'" ~ P(Z)
Z~A
ofC [G] lies in fact in Q [G], and is an indecomposable central idempotent
in Q [G]. Every indecomposable central idempotent in Q [G] is of this
form. We have
(4.4.0.3)
p(A)P(A,)=~P(A)
if
A=A'
O
if not.
(4.4.0.4)
Let Hz be a local system of Zmodules of finite type on which
G acts. We define the Gsublocal system
(4.4.0.5)
P(A) H z
de_~f'n
the inverse image in H z of
P(A)(Ho) ~ HQ.
The canonical mapping of local systems
(4.4.0.6)
(~ P(A) H z ~ H z
A
is a Gmorphism and an
isogeny,
i.e., it becomes an isomorphism when
tensored with Q.
(4.4.1)
If G acts on a family of mixed Hodge structures (H z, W,F)
(meaning that its action on the local system Hz respects W and F), then
each P(A) H z is a subfamily of mixed Hodge structures. If (H z, W, F) is
a polarizable (4.2.2.4) family of mixed Hodge structures, so is each sub
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
 Fall '11
 NormanKatz

Click to edit the document details