Ring of integers

About: Ring of integers is a research topic. Over the lifetime, 1856 publications have been published within this topic receiving 15882 citations.

The structure of the group of permutations induced by Chebyshev polynomial vectors over the ring of integers mod m

Abstract: In an earlier paper the author investigated the properties of a class of multivanable polynomial vectors which generalise the multivariable Chebyshev polynomial vectors. In this paper the behaviour of these polynomials over rings of the type Z/(m) is investigated, and conditions are determined for such an n -variable polynomial vector to induce a permutation of (Z/(m)) n . More detailed results on the Chebyshev polynomial vectors follow. The composition properties of these vectors imply that the permutations induced by certain subsets of them form groups under composition of mappings, and the structure of these groups is investigated.

On the trace of the ring of integers of an abelian number field

Abstract: and the OK-ideal T (OL) ⊆ OK . By I(L/K) we denote the group index of T (OL) in OK (i.e., the norm of T (OL) over Q). It seems to be difficult to determine I(L/K) in the general case. If K and L are absolutely abelian number fields, however, we obtain a fairly explicit description of the number I(L/K). This is a consequence of our description of the Galois module structure of T (OL) (Theorem 1). The case of equal conductors fK = fL of the fields K, L is of particular interest. Here we show that I(L/K) is a certain power of 2 (Theorems 2, 3, 4).

Finite flat models of constant group schemes of rank two

Abstract: We calculate the number of the isomorphism class of the finite flat models over the ring of integers of an absolutely ramified $p$-adic field of constant group schemes of rank two over finite fields, by counting the rational points of a moduli space of finite flat models.

Unicity of types for supercuspidals

Abstract: Let $F$ be a non-Archimedean local field, with the ring of integers $\mathfrak{o}_F. Let $G=GL_N(F)$, $K=GL_N(\mathfrak{o}_F)$ and $\pi$ a supercuspidal representation of $G$. We show that there exist a unique irreducible smooth representation $\tau$ of $K$, such that the restriction to $K$ of a smooth irreducible representation $\pi'$ of $G$ contains $\tau$ if and only if $pi'$ is isomorphic to $\pi\otimes\chi\circ\det$, where $\chi$ is an unramified quasicharacter of $F^{\times}$. Moreover, we show that $\pi$ contains $\tau$ with the multiplicity 1. As a corollary we obtain a kind of inertial local Langlands correspondence.