Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N = 1 supersymmetric Hirota operators. Using them, we bilinearize SUSY nonlinear evolution equations. The super-soliton solutions and extension to SUSY sine-Gordon are also discussed. As a quite strange paradox it is shown that the Lax integrable SUSY KdV of Manin-Ra...

Sixty children, aged between 2 and 10 years, had boutonneuse fever during the summer months of 1979 and 1980. They presented with fever and a generalised maculopapular rash. The tàche noire could be seen at the site of the tick bite in 38 (63%) of them. The antibody response, assayed nonspecifically, by the Weil-Felix reaction was positive in 52. A singe titre of more than 1:80 or a 4-fold incr...

We show that there exist genus one curves of every index over the rational numbers, answering affirmatively a question of Lang and Tate. The proof is “elementary” in the sense that it does not assume the finiteness of any Shafarevich-Tate group. On the other hand, using Kolyvagin’s construction of a rational elliptic curve whose Mordell-Weil and Shafarevich-Tate groups are both trivial, we show...

We study the growth of the Mordell-Weil groups E(Kn) of an elliptic curve E as Kn runs through the intermediate fields of a Zp-extension. We describe those Zp-extensions K∞/K where we expect the ranks to grow to infinity. In the cases where we know or expect the rank to grow, we discuss where we expect to find the submodule of universal norms. 2000 Mathematics Subject Classification: Primary 11...

We prove that the triviality of the Galois action on the suitably twisted odd-dimensional étale cohomogy group with finite coefficients of an absolutely irreducible smooth projective variety implies the existence of certain primitive roots of unity in the field of definition of the variety. This text was inspired by an exercise in Serre’s Lectures on the Mordell–Weil theorem.

The following divisors in the space Sym12 P1 of twelve points on P 1 are actually the same: (A) The possible locus of the twelve nodal fibers in a rational elliptic fibration (i.e. a pencil of plane cubic curves); (B) degree 12 binary forms that can be expressed as a cube plus a square; (C) the locus of the twelve tangents to a smooth plane quartic from a general point of the plane; (D) the bra...

We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use...

Let K be an algebraically closed field, X a smooth projective variety over K and f : X → X a dominant regular morphism. Let N (X) be the group of algebraic cycles modulo numerical equivalence. Let χ(f) be the spectral radius of the pullback f∗ : H∗(X,Ql) → H ∗(X,Ql) on l-adic cohomology groups, and λ(f) the spectral radius of the pullback f∗ : N∗(X) → N∗(X). We prove in this paper, by using con...

1. Smooth Manifolds: 9/22/14 1 2. Going on a Tangent (Space): 9/24/14 1 3. Immersions and Embeddings: 9/26/14 3 4. Riemannian Metrics: 9/29/14 3 5. Indiana Jones and the Isometries of the Upper Half-Plane: 10/1/14 5 6. That's an Affine Connection You've Got There: 10/3/14 7 7. Missed (Levi-Civita) Connections: 10/6/14 9 8. The Levi-Civita Connection and the Induced Metric: 10/8/14 9 9. Geodesic...

The World Health Organization/Food and Agricultural Organization Collaborating Centre for Reference and Research on Leptospirosis, Western Pacific Region, accredited since 1958, is part of Queensland Health Scientific Services, which provide tertiary level support in epidemiology, surveillance, training and diagnosis for hospitals and pathology laboratories across the State. Databases for lepto...