Let q be a prime power and let Fq be the nite eld with q elements. For each polynomial Q(T) in FqT ], one could use the Carlitz module to construct an abelian extension of Fq(T), called a Carlitz cyclotomic extension. Carlitz cyclotomic extensions play a fundamental role in the study of abelian extensions of Fq(T), similar to the role played by cyclotomic number elds for abelian extensions of Q...

Given a 3-uniform hypergraph H, subset M of V(H) is module H if for each $$e\in E(H)$$ e ∈ E ( ) such that $$e\cap M\ne \emptyset$$ ∩ ≠ ∅ and $$e\setminus \ , there exists $$m\in M$$ m M=\{m\}$$ = { } every $$n\in n we have $$(e\setminus \{m\})\cup \{n\}\in ∪ . For example, $$\emptyset$$ $$\{v\}$$ v where $$v\in V(H)$$ V are modules called trivial. A prime all its hypergraph, study prime, induc...

For an elliptic curve E over ℚ, putting K=ℚ(E[p]) which is the p-th division field of for odd prime p, we study ideal class group ClK K as a Gal(K/ℚ)-module. More precisely, any j with 1⩽j⩽p-2, give condition that ClK⊗Fp has symmetric power SymjE[p] E[p] its quotient Gal(K/ℚ)-module, in terms Bloch-Kato’s Tate-Shafarevich SymjVpE. Here VpE denotes rational p-adic Tate module E. This partial gen...

Let G be a connected reductive group G over an algebraically closed field k of prime characteristic p, and g = Lie(G). In this paper, we study modular representations of the reductive Lie algebra g with p-character χ of standard Levi-form associated with an index subset I of simple roots. With aid of support variety theory we prove a theorem that a Uχ(g)-module is projective if and only if it i...

For a space X, we define Frobenius and Verschiebung operations on the nil-terms NAfd ± (X) in the algebraic K-theory of spaces, in three different ways. Two applications are included. Firstly, we obtain that the homotopy groups of NAfd ± (X) are either trivial or not finitely generated as abelian groups. Secondly, the Verschiebung defines a Z[N×]-module structure on the homotopy groups of NAfd ...

The multiplicative inversion operation is a fundamental computation in several cryptographic applications. In this work, we propose a scalable VLSI hardware to compute the Montgomery modular inverse in GF(p). We suggest a new correction phase for a previously proposed almost Montgomery inverse algorithm to calculate the inversion in hardware. We also propose an efficient hardware algorithm to c...

We define Frobenius and Verschiebung operations on the A-theoretic nil-terms NA ± (X) for a space X in three different ways. Two applications are included. Firstly, we obtain that the homotopy groups of NA ± (X) are either trivial or not finitely generated as abelian groups. Secondly, the Verschiebung defines a Z[N×]-module structure on the homotopy groups of NA ± (X), with N× the multiplicativ...

The hit problem for a cohomology module over the Steenrod algebra A asks for a minimal set of A-generators for the module. In this paper we consider the symmetric algebras over the field Fp, for p an arbitrary prime, and treat the equivalent problem of determining the set of A∗-primitive elements in their duals. We produce a method for generating new primitives from known ones via a new action ...

The Montgomery inversion is a fundamental computation in several cryptographic applications. In this work, we propose a scalable hardware architecture to compute the Montgomery modular inverse in GF(p). We suggest a new correction phase for a previously proposed almost Montgomery inverse algorithm to calculate the inversion in hardware. The intended architecture is scalable, which means that a ...