...
On the periods of motives
with complex multiplication
and a conjecture of Gross-
Deligne
By Vincent Maillot and Damian Roessler
ON THE PERIODS OF MOTIVES WITH COMPLEX MULTIPLICATION
745
When ... slight variation of results by Anderson, Colmez
and Gross on the periods of CM abelian varieties is valid for a larger class of
CM motiv...
... rational maps with Siegel disks; see for example [P2] and [Mc2] for
the case of quadratic polynomials, and [Z1] and [YZ] for variants in the case
of cubic polynomials and quadratic rational maps.
3.2. ... reaches the boundary of a drop U of minimal generation. It then follows
the boundary of U along a nontrivial arc I. Finally, it returns along the
boundaries...
... P
|W
a
1
(ct) ∩ W
a
2
(ct)|≥t
= −I
κ
a
d
(c)
and derive a variational representation for the rate constant I
κ
a
d
(c). Here, κ
a
is the Newtonian capacity of the ball with radius a. We show that ... intersection volume may either increase or decrease when
the Wiener sausages are wrapped around Λ
N
, so there is no simple comparison
available.
Proof. The proof...
... M
U,V
.
Proof. In Proposition 4.1 we established surjectivity of the linearization
of the map (6). An application of the implicit function theorem with J ∈J
U,V
and a
0
as parameters thus establishes ... certain fibers F
a
and with
¯
C
∼ dH +(k −
m
a
)F . The space of such
configurations is of real codimension 2d
a
m
a
. Therefore Z is a union of su...
... good, planar Zappatic surface,
E =
˜
E and the 1-skeleton G
(1)
X
of G
X
coincides with the dual graph G
D
of the
general hyperplane section D of X.
As a straightforward generalization of what we ... Graph associated to an impossible planar Zappatic surface.
that G
X
= G, the 2-skeleton of G has to consist of the face bounded by the
1-skeleton.
We can also consid...
... prove that the b-ary expansion of every
irrational algebraic number cannot have low complexity. Furthermore, we es-
tablish that irrational morphic numbers are transcendental, for a wide class
of ... who made the conjecture that such an expansion should
satisfy some of the same laws as do almost all real numbers. In particular, it
is expected that every irrational algebraic nu...
... in particular
harmonic analysis of Boolean functions and extremal set theory.
For the rest of the paper, we will adopt the notation of extremal set
theory as follows. A family of subsets of a finite ... projection constraints, a value for the x variable has only one
possible extension to a value for the y variable; but a value for the y variable
may leave many...
... Perron-Frobenius theorem through
the contraction of cones of ‘real-analytic’ functions. The pressure function may
then be calculated as the averaged action of the operator on a hyperbolic fixed
point ... Julia set on the Riemann
sphere we show that if the family of maps and the probability law depend real-
analytically on parameters then so does its almost sure...
... exists a simple, separable, unital, and nuclear
C
∗
-algebra A such that for any UHF algebra U and any F ∈Fone has
F (A)
∼
=
F (A ⊗U),
yet A and A ⊗U are not isomorphic. A is moreover an approximately ... homo-
geneous (AH) algebra, and A ⊗U is an approximately interval (AI) algebra.
Theorem 1.2. There exist a simple, separable, unital, and nuclear
C
∗
-algebra B an...
... measurements were done
for each donor concentration, and the average was fitted to
the sum of two exponentials. The observed rate constant
from the fast phase of this double-exponential decay was
plotted ... detergent
in one of the chromatographic steps of the standard
purification procedure (see Materials and methods): prior
to gel filtration, the partially purified mat...