Let k be a number field, let E/k be an elliptic curve, and let S be a finite set of places of k containing the archimedean places. We prove that if α ∈ E(k) is nontorsion, then there are only finitely many torsion points ξ ∈ E(k)tors which are S-integral with respect to α. We also prove an analogue of this for the multiplicative group, and formulate conjectural generalizations for abelian varie...

Let A be an abelian variety over the function field K of a compact Riemann surface B. Fix model $$f :{\mathcal {A}} \rightarrow B$$ A/K and effective horizontal divisor $${\mathcal {D}}\subset {\mathcal {A}}$$ . We give sufficient condition on {D}}$$ for finiteness set $$(S, {D}})$$ -integral sections every finite subset $$S \subset These integral $$\sigma $$ are algebraic satisfy geometric ( \...

The construction of supersymmetric invariant integrals is discussed in a superspace setting. The formalism is applied to D = 4, N = 4 SYM and used to construct the F 2 , F 4 and (F 5 + ∂ 2 F 4) terms in the effective action of coincident D-branes. The results are in agreement with those obtained by other methods. A simple derivation of the abelian ∂ 4 F 4 invariant is given and generalised to t...

The theme of doing quantum mechanics on all abelian groups goes back to Schwinger and Weyl. If the group is a vector space of finite dimension over a non-archimedean locally compact division ring, it is of interest to examine the structure of dynamical systems defined by Hamiltonians analogous to those encountered over the field of real numbers. In this letter a path integral formula for the im...

Among the class of finite integral commutative residuated chains (ICRCs), we identify those algebras which can be obtained as a nuclear retraction of a conuclear contraction of a totally ordered Abelian l-group. We call the ICRCs satisfying this condition regular. Then we discuss the structure of finite regular ICRCs. Finally, we prove that the class of regular members generate a strictly small...

In this note we investigate the hypercentral units in integral group rings ZG, where G is not necessarily torsion. One of the main results obtained is the following (Theorem 3.5): if the set of torsion elements of G is a subgroup T of G and if Z2(U) is not contained in CU (T ), then T is either an Abelian group of exponent 4 or a Q∗ group. This extends our earlier result on torsion group rings.

If K/k is a finite Galois extension of number fields with Galois group G, then the kernel of the capitulation map Clk ~ ClK of ideal class groups is isomorphic to the kernel X(H) of the transfer map H/H’ ~ A, where H = Gal(K/k), A = Gal(K/K) and K is the Hilbert class field of K. H. Suzuki proved that when G is abelian, |G| divides |X(H)|. We call a finite abelian group X a transfer kernel for ...

The string representation of the Abelian projected SU(3)-gluodynamics partition function is derived by using the path-integral duality transformation. On this basis, we also derive analogous representations for the generating functionals of correlators of gluonic field strength tensors and monopole currents, which are finally applied to the evaluation of the corresponding bilocal correlators. T...

We describe a new algebraically completely integrable system, whose integral manifolds are co-elliptic subvarieties of Jacobian varieties. This is a multi-periodic extension of the Krichever-Treibich-Verdier system, which consists of elliptic solitons. The goal of this work is to generalize the theory of elliptic solitons, which was developed by A. Treibich and J.-L. Verdier based on earlier wo...

A formula constituting the non-Abelian Stokes theorem for general semi-simple compact gauge groups is presented. The formula involves a path integral over a group space and is applicable to Wilson loop variables irrespective of the topology of loops. Some simple expressions analogous to the ’t Hooft tensor of a magnetic monopole are given for the 2-form of interest. A special property in the ca...