Dear
Sasha,
I am
writing
this
letter
to put
in order
at least
some
of the
intuitiv
e ideas
about
the
theory
of mixed
motiv
es,
whic
h I have in mind.
What
I really
would
like to discuss
with
you
is the
hypothesis
(0.0.25),
but
unfortunately
to form
ulate
it I have to start
with
more
elemen
tary
matters.
In this
text
there
are
four
types of statemen
ts:
Theorem
is something
I've pro
ven
and
really
wrote
down.
Pretheorem
is a statmen
t whic
h I believ
e I've pro
ven
but
whic
h is not
carefully
written
yet.
Conjecture
is a statemen
t whic
h I believ
e I kno
w how to pro
ve.
Hyp
othesis
is something
I just
would
like to be true.
All
through
this
text
I consider
only
the
case
of rational
coecien
ts,
i.e.
all
additiv
e categories
are
supp
osed
to be
Q
-linear.
For a cohomological
functor
H
i
:
D

X
i
=0
x
i
= 1
n
Y
i
=0
x
i
= 0
in the
ane
space
A
n
+1
k
. We will
consider
it as We will
consider
it as (
n