We confirm a conjecture of Merel describing a certain relation between the jacobians of various quotients of X(p) in terms of specific correspondences.

Algebraic geometrical solutions of a new shallow-water equation and Dymtype equation are studied in connection with Hamiltonian flows on nonlinear subvarieties of hyperelliptic Jacobians. These equations belong to a class of N -component integrable systems generated by Lax equations with energydependent Schrödinger operators having poles in the spectral parameter. The classes of quasi-periodic ...

The aim here is to continue the investigation in [1] of Jacobians of a Klein surface and also to correct an error in [1].

For every $n$-dimensional smooth projective variety $X$ over ℂ, the motive $M(X)$ is expected to admit a Chow-Künneth decomposition $M_0(X)\oplus \cdots \oplus M_{2n}(X)$. Inspired by slice filtration of we propose definitions $M_2(X)$ and $M_{2n-2}(X)$. In our construction use intermediate Jacobians.

Let p be an odd prime. Let K be a field of characteristic zero and Ka its algebraic closure. Let n ≥ 5 and m ≥ 5 be integers. Let f(x), h(x) ∈ K[x] be irreducible separable polynomials of degree n and m respectively. Suppose that the Galois group of f is either the full symmetric group Sn or the alternating group An and the Galois group of h is either the full symmetric group Sm or the alternat...

The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from Cart(Ω,Rm) is approximated by C functions strongly in A(Ω,R) whenever q < p. An example is shown of a function which is in cart(Ω,R) but not in cart(Ω,R).