402 research outputs found
Modular curves and N\'eron models of generalized Jacobians
Let be a smooth geometrically connected projective curve over the field
of fractions of a discrete valuation ring , and a modulus on
, given by a closed subscheme of which is geometrically reduced. The
generalized Jacobian of with respect to is
then an extension of the Jacobian of by a torus. We describe its N\'eron
model, together with the character and component groups of the special fibre,
in terms of a regular model of over . This generalizes Raynaud's
well-known description for the usual Jacobian. We also give some computations
for generalized Jacobians of modular curves with moduli supported on
the cusps.Comment: 36 pages, minor corrections and references added. Accepted version,
to appear in Compositio Mat
Quantum well infrared photodetectors hardiness to the non ideality of the energy band profile
We report results on the effect of a non-sharp and disordered potential in
Quantum Well Infrared Photodetectors (QWIP). Scanning electronic transmission
microscopy is used to measure the alloy profile of the structure which is shown
to present a gradient of composition along the growth axis. Those measurements
are used as inputs to quantify the effect on the detector performance (peak
wavelength, spectral broadening and dark current). The influence of the random
positioning of the doping is also studied. Finally we demonstrate that QWIP
properties are quite robust with regard to the non ideality of the energy band
profile
Numerical evidence toward a 2-adic equivariant ''Main Conjecture''
International audienceWe test a conjectural non abelian refinement of the classical 2-adic Main Conjecture of Iwasawa theory. In the first part, we show how, in the special case that we study, the validity of this refinement is equivalent to a congruence condition on the coefficients of some power series. Then, in the second part, we explain how to compute the first coefficients of this power series and thus numerically check the conjecture in that setting
Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence
We study indefinite quaternion algebras over totally real fields F, and give
an example of a cohomological construction of p-adic Jacquet-Langlands
functoriality using completed cohomology. We also study the (tame) levels of
p-adic automorphic forms on these quaternion algebras and give an analogue of
Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the
published versio
Endomorphisms of superelliptic jacobians
Let K be a field of characteristic zero, n>4 an integer, f(x) an irreducible
polynomial over K of degree n, whose Galois group is doubly transitive simple
non-abelian group. Let p be an odd prime, Z[\zeta_p] the ring of integers in
the p-th cyclotomic field,
C_{f,p}:y^p=f(x) the corresponding superelliptic curve and J(C_{f,p}) its
jacobian. Assuming that either n=p+1 or p does not divide n(n-1), we prove that
the ring of all endomorphisms of J(C_{f,p}) coincides with Z[\zeta_p].Comment: Several typos have been correcte
Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields
We study the arithmetic of Eisenstein cohomology classes (in the sense of G.
Harder) for symmetric spaces associated to GL_2 over imaginary quadratic
fields. We prove in many cases a lower bound on their denominator in terms of a
special L-value of a Hecke character providing evidence for a conjecture of
Harder that the denominator is given by this L-value. We also prove under some
additional assumptions that the restriction of the classes to the boundary of
the Borel-Serre compactification of the spaces is integral. Such classes are
interesting for their use in congruences with cuspidal classes to prove
connections between the special L-value and the size of the Selmer group of the
Hecke character.Comment: 37 pages; strengthened integrality result (Proposition 16), corrected
statement of Theorem 3, and revised introductio
Modular symbols in Iwasawa theory
This survey paper is focused on a connection between the geometry of
and the arithmetic of over global fields,
for integers . For over , there is an explicit
conjecture of the third author relating the geometry of modular curves and the
arithmetic of cyclotomic fields, and it is proven in many instances by the work
of the first two authors. The paper is divided into three parts: in the first,
we explain the conjecture of the third author and the main result of the first
two authors on it. In the second, we explain an analogous conjecture and result
for over . In the third, we pose questions for general
over the rationals, imaginary quadratic fields, and global function fields.Comment: 43 page
Midwave infrared InAs/GaSb superlattice photodiode with a dopant-free pân junction
Midwave infrared (MWIR) InAs/GaSb superlattice (SL) photodiode with a dopant-free pân junction was fabricated by molecular beam epitaxy on GaSb substrate. Depending on the thickness ratio between InAs and GaSb layers in the SL period, the residual background carriers of this adjustable material can be either n-type or p-type. Using this flexibility in residual doping of the SL material, the pân junction of the device is made with different non-intentionally doped (nid) SL structures. The SL photodiode processed shows a cut-off wavelength at 4.65 ÎŒm at 77 K, residual carrier concentration equal to 1.75 Ă 1015 cmâ3, dark current density as low as 2.8 Ă 10â8 A/cm2 at 50 mV reverse bias and R0A product as high as 2 Ă 106 Ω cm2. The results obtained demonstrate the possibility to fabricate a SL pin photodiode without intentional doping the pn junction
Equidistribution of Heegner Points and Ternary Quadratic Forms
We prove new equidistribution results for Galois orbits of Heegner points
with respect to reduction maps at inert primes. The arguments are based on two
different techniques: primitive representations of integers by quadratic forms
and distribution relations for Heegner points. Our results generalize one of
the equidistribution theorems established by Cornut and Vatsal in the sense
that we allow both the fundamental discriminant and the conductor to grow.
Moreover, for fixed fundamental discriminant and variable conductor, we deduce
an effective surjectivity theorem for the reduction map from Heegner points to
supersingular points at a fixed inert prime. Our results are applicable to the
setting considered by Kolyvagin in the construction of the Heegner points Euler
system
Radiometric and noise characteristics of InAs-rich T2SL MWIR pin photodiodes
We present a full characterization of the radiometric performances of a type-II InAs/GaSb superlattice pin photodiode operating in the mid-wavelength infrared domain. We first focused our attention on quantum efficiency, responsivity and angular response measurements: quantum efficiency reaches 23% at λ = 2.1 ”m for 1 ”m thick structure. Noise under illumination measurements are also reported: noise is limited by the Schottky contribution for reverse bias voltage smaller than 1.2 V. The specific detectivity, estimated for 2p field-of-view and 333 K background temperature, was determined equal to 2.29 x 10^10 Jones for -0,8 V bias voltage and 77 K operating temperature
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