3,990 research outputs found
Some genus 3 curves with many points
Using an explicit family of plane quartic curves, we prove the existence of a
genus 3 curve over any finite field of characteristic 3 whose number of
rational points stays within a fixed distance from the Hasse-Weil-Serre upper
bound. We also provide an intrinsic characterization of so-called Legendre
elliptic curves
Galois Theory, discriminants and torsion subgroups of elliptic curves
We find a tight relationship between the torsion subgroup and the image of
the mod 2 Galois representation associated to an elliptic curve defined over
the rationals. This is shown using some characterizations for the squareness of
the discriminant of the elliptic curve.Comment: New version, some typos fixed and the proof of the lemma in the
Appendix has been expande
Chute stationnaire d\u27un solide dans un fluide visqueux incompressible le long d\u27un plan incliné
Extended diffeomorphism algebras in (quantum) gravitational physics
We construct an explicit representation of the algebra of local
diffeomorphisms of a manifold with realistic dimensions. This is achieved in
the setting of a general approach to the (quantum) dynamics of a physical
system which is characterized by the fundamental role assigned to a basic
underlying symmetry. The developed mathematical formalism makes contact with
the relevant gravitational notions by means of the addition of some extra
structure. The specific manners in which this is accomplished, together with
their corresponding physical interpretation, lead to different gravitational
models. Distinct strategies are in fact briefly outlined, showing the
versatility of the present conceptual framework.Comment: 20 pages, LATEX, no figure
Effective string picture for confinement at finite temperature: theoretical predictions and high precision numerical results
The effective string picture of confinement is used to derive theoretical
predictions for the interquark potential at finite temperature. At short
distances, the leading string correction to the linear confining potential
between a heavy quark-antiquark pair is the "L\"uscher term''. We assume a
Nambu--Goto effective string action, and work out subleading contributions in
an analytical way. We discuss the contribution given by a possible ``boundary
term'' in the effective action, comparing these predictions with results from
simulations of lattice gauge theory in three dimensions, obtained with an
algorithm which exploits the duality of the gauge model with the Ising
spin model.Comment: Lattice2003(nonzero), 3 pages, 2 figure
Alternating groups and moduli space lifting Invariants
Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of
degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves
Fried-Serre on deciding when sphere covers with odd-order branching lift to
unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on
Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces
of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp.
odd) theta functions when r is even (resp. odd). For inner spaces the result is
independent of r. Another use appears in,
http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of
families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for
the prime p=2 lying over Hurwitz spaces first studied by,
http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and
Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*)
High tower levels are general-type varieties and have no rational points.For
infinitely many of those MTs, the tree of cusps contains a subtree -- a spire
-- isomorphic to the tree of cusps on a modular curve tower. This makes
plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs.
Establishing these modular curve-like properties opens, to MTs, modular
curve-like thinking where modular curves have never gone before. A fuller html
description of this paper is at
http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from
proof sheets, but does include some proof simplification in \S
Representations and -theory of Discrete Groups
Let be a discrete group of finite virtual cohomological dimension
with certain finiteness conditions of the type satisfied by arithmetic groups.
We define a representation ring for , determined on its elements of
finite order, which is of finite type. Then we determine the contribution of
this ring to the topological -theory , obtaining an exact
formula for the difference in terms of the cohomology of the centralizers of
elements of finite order in .Comment: 4 page
Invariance Properties of Inviscid Fluids of Grade n
Revisited and completed version, 18 pages and 2 figures.International audienceFluids of grade n are continuous media in dynamic changes of phases avoiding the surfaces of discontinuity and representing the capillary layers in liquid-vapour interfaces. We recall the thermodynamic form of the equation of motion for inviscid fluids of grade n. First integrals and theorems of circulation are deduced. A general classification of flows is proposed
On a differential inclusion related to the Born-Infeld equations
We study a partial differential relation that arises in the context of the
Born-Infeld equations (an extension of the Maxwell's equations) by using
Gromov's method of convex integration in the setting of divergence free fields
On p-adic lattices and Grassmannians
It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive
group G over a field k, carry the geometric structure of an inductive limit of
projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for
G. From the point of view of number theory it would be interesting to obtain an
analogous geometric interpretation of quotients of the form
G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of
p-typical Witt vectors, k is a perfect field of characteristic p and G is a
reductive group scheme over W(k). The present paper is an attempt to describe
which constructions carry over from the function field case to the p-adic case,
more precisely to the situation of the p-adic affine Grassmannian for the
special linear group G=SL_n. We start with a description of the R-valued points
of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R),
where R is a perfect k-algebra. In order to obtain a link with geometry we
further construct projective k-subvarieties of the multigraded Hilbert scheme
which map equivariantly to the p-adic affine Grassmannian. The images of these
morphisms play the role of Schubert varieties in the p-adic setting. Further,
for any reduced k-algebra R these morphisms induce bijective maps between the
sets of R-valued points of the respective open orbits in the multigraded
Hilbert scheme and the corresponding Schubert cells of the p-adic affine
Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math.
Zeitschrift, of the previously published preprint "On p-adic loop groups and
Grassmannians
- …