arithmetic theory of elliptic curves - j coates
arithmetic theory of elliptic curves - j. coates
...
Much of the recent research in the arithmetic of elliptic curves consists
in the study of modularity properties of elliptic curves over Q, or of the
structure of the Mordell-Weil group E(K) of ... USA
94
(1997), 1111 5-1 1117.
J. Coates, S. Howson, Euler characteristics and elliptic curves 11, in prepara-
tion.
J. Coates, R. Sujatha, Galois cohomology...
Đề tài " Finding large Selmer rank via an arithmetic theory of local constants " docx
... that W is an R-module and B is a Z
p
-module.
Composition with τ ⊗ 1:R⊗
Z
p
B → B gives a bijection between the set of
R-semilinear pairings W × W →R⊗
Z
p
B, and the set of ι-adjoint pairings
W ... Hom
R
(W, Hom
Z
p
(W
ι
,B)).(A.2)
The left-hand side is the set of R-semilinear pairings W × W →R⊗
Z
p
B, and
the right-hand side is the set of ι-adjoint pairings W × W → B.
Since compositi...
moduli of curves - j. harris, i. morrison
... universal family of lines
over P
1
?
Exercise (1.6) 1) Show that the j- line M
1
is a coarse moduli space
for curves of genus 1.
2) Show that a j- function J on a scheme B arises as the j- function
associated ... ge-
ometry of families of our moduli problem and information about the
geometry of the moduli space M itself. One of the main themes of
moduli theory is to bri...
elliptic curves - notes for math 679 - j. milne, u. michigan
... number of variables
over any number field K (Hasse-Minkowski theorem). There is a very down-to-earth proof
of the original case of the theorem in [C2]—it takes three lectures. A good exposition of
the ... on affine curves
Regular functions on projective curves
The Riemann-Roch theorem
The group law revisited
Perfect base fields
5. Definition of an Elliptic Curve 19
Plane projective...
mendonc,a j.t. theory of photon acceleration
... ultra-short laser pulse prop-
agation [3, 23], or to new particle accelerator concepts and new sources of radia-
tion [42]. The concept of photon acceleration can then be seen as a kind of new
theoretical ... timescale
of a few tens of femtoseconds, can still be considered as slow processes in the
Description of the contents
7
optical domain and stay within the range of validity...
The theory of financial intermediation: An essay on what it does (not) explain
... Clemens Grafe, Central Banking and the Choice
of Currency Regime in Accession Countries, Vienna, 2001,
ISBN 3-9 0 2-1 0 9-0 3-3 .
12. Sanjiva Prasad, Christopher J. Green, and Victor Murinde, Company
Financing, ... Economies, Vienna, 2001, ISBN 3-9 0210 9-0 4-1 .
13. Martin M.G. Fase, Investment in Paintings: The interaction of monetary
return and psychic income, Vienna, 2...
Circuit theory of finance and the role of incentives in financial sector reform
... −
(A.7) c c
w k
= α
(A.8) c y s
i i i
= −
(A.9a) ),(
, Ljjkij
ryss =
=
(A.9b) (.,.)]1),([
jLjjj
zrzss −+= υ
(A.10)
Lj
rzr =
(A.11)
∑
=
−=
Fbfjih
hh
szD
,,,,
)1(
(A.12a) )(
−
−=
L
dd
rII µ
(A.12b) ... cause of the excessive growth in short-term lending to the
region. At a time of over-heating and over-optimistic expectations, short-term lenders - typically
less concerned with the long...
Theory of stochastic local area channel modeling for wireless communications
... FIRST-ORDER STATISTICS OF SMALL-SCALE CHANNELS 96
4.3.3 The Three-Wave PDF
Two- and Three-Wave models often are used to describe fading in microwave digital radio
communications [30]. The Three-Wave ... approach. Recall from
probability theory that if a real-valued random variable, Z, is the sum of a set of independent
CHAPTER 4. FIRST-ORDER STATISTICS OF SMALL-SCALE CHANNELS 116
wh...
Complexity Theory of Transforms in Signal Processing
... numbers). For non-negative integers k
j
,letT(k
j
,F
j
,P
j
) denote the task of computing
k
j
products of arbitrary polynomials by F
j
modulo P
j
.Let
j
T(k
j
,F
j
,P
j
) denote the task of
simultaneously ... computing all of these products. If the coefficients span a vector space of dimension
j
d
j
over φ, then the multiplicative complexity of
j...
Theory of rapid granular flows Isaac Goldhirsch
... form
Q
i
=−˜κn
√
T
∂T
∂r
i
−
˜
λ
√
T
3
∂n
∂r
i
+
˜
θ
1
n
2
∂V
j
∂r
j
∂T
∂r
i
+
˜
θ
2
n
2
2
3
∂
∂x
i
T
∂V
j
∂r
j
+ 2
∂V
j
∂r
i
∂T
∂r
j
+
˜
θ
3
2
∂V
j
∂r
i
∂(nT)
∂r
j
+
˜
θ
4
n
2
T
∂
2
V
j
∂r
i
∂r
j
+
˜
θ
5
n
2
∂V
j
∂r
i
∂T
∂r
j
, (12.32)
where ... P
ij
∂r
j
= 0, (12.7)
n
DT
Dt
+ 2
∂V
i
∂r
j
P
ij
+ 2
∂ Q
j
∂r
j
=−n, (12.8)
12.3 Kinetic theory 1...