30 research outputs found
Big Line Bundles over Arithmetic Varieties
We prove a Hilbert-Samuel type result of arithmetic big line bundles in
Arakelov geometry, which is an analogue of a classical theorem of Siu. An
application of this result gives equidistribution of small points over
algebraic dynamical systems, following the work of Szpiro-Ullmo-Zhang. We also
generalize Chambert-Loir's non-archimedean equidistribution
SU(2) WZW Theory at Higher Genera
We compute, by free field techniques, the scalar product of the SU(2)
Chern-Simons states on genus > 1 surfaces. The result is a finite-dimensional
integral over positions of ``screening charges'' and one complex modular
parameter. It uses an effective description of the CS states closely related to
the one worked out by Bertram. The scalar product formula allows to express the
higher genus partition functions of the WZW conformal field theory by
finite-dimensional integrals. It should provide the hermitian metric preserved
by the Knizhnik-Zamolodchikov-Bernard connection describing the variations of
the CS states under the change of the complex structure of the surface.Comment: 44 pages, IHES/P/94/10, Latex fil
Special values of canonical Green's functions
We give a precise formula for the value of the canonical Green's function at
a pair of Weierstrass points on a hyperelliptic Riemann surface. Further we
express the 'energy' of the Weierstrass points in terms of a spectral invariant
recently introduced by N. Kawazumi and S. Zhang. It follows that the energy is
strictly larger than log 2. Our results generalize known formulas for elliptic
curves.Comment: 10 page
Correspondences in Arakelov geometry and applications to the case of Hecke operators on modular curves
In the context of arithmetic surfaces, Bost defined a generalized Arithmetic
Chow Group
(ACG) using the Sobolev space L^2_1. We study the behavior of these groups
under pull-back and push-forward and we prove a projection formula.
We use these results to define an action of the Hecke operators on the ACG of
modular curves and to show that they are self-adjoint with respect to the
arithmetic intersection product. The decomposition of the ACG in
eigencomponents which follows allows us to define new numerical invariants,
which are refined versions of the self-intersection of the dualizing sheaf.
Using the Gross-Zagier formula and a calculation due independently to Bost and
Kuehn we compute these invariants in terms of special values of L series. On
the other hand, we obtain a proof of the fact that Hecke correspondences acting
on the Jacobian of the modular curves are self-adjoint with respect to the
N\'eron-Tate height pairing.Comment: 38 pages. Minor correction
Mechanism of cellular rejection in transplantation
The explosion of new discoveries in the field of immunology has provided new insights into mechanisms that promote an immune response directed against a transplanted organ. Central to the allograft response are T lymphocytes. This review summarizes the current literature on allorecognition, costimulation, memory T cells, T cell migration, and their role in both acute and chronic graft destruction. An in depth understanding of the cellular mechanisms that result in both acute and chronic allograft rejection will provide new strategies and targeted therapeutics capable of inducing long-lasting, allograft-specific tolerance