Abstract In supersingular isogeny-based cryptography, the path-finding problem reduces to endomorphism ring problem. Can be reduced knowing just one endomorphism? It is known that a small degree enables polynomial-time and computation (in: Love Boneh, ANTS XIV-Proceedings of Fourteenth Algorithmic Number Theory Symposium, volume 4 Open Book Ser. Math. Sci. Publ., Berkeley, 2020). An gives an ex...

As usual, we write Z,Q,Fp,C for the ring of integers, the field of rational numbers, the finite field with p elements and the field of complex numbers respectively. If Z is a smooth algebraic variety over an algebraically closed field then we write Ω(Z) for the space of differentials of the first kind on Z. If Z is an abelian variety then we write End(Z) for its ring of (absolute) endomorphisms...

In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures with a single m-ary relation for any m ∈ N over a finite set. We use this recipe to determine the automorphism groups of the following semigroups: the full transformation semigroup, the partial transformation semigroup, and the symmetric in...

A seminear-ring is a generalization of ring. In ring theory, if with the multiplicative identity, then endomorphism module isomorphic to . Let be seminear-ring. Here, we can construct set from itself denoted by We show that seminear-ring, also over addition and composition function. will apply congruence relation get quotient endomorphism. Furthermore, between c-ideal relations. So, c-ideal.

1.1. Let Fq be a finite field of characteristic p, let k be an algebraic closure of Fq, and let X/Fq be a separated, normal, 2-dimensional Fq-scheme of finite type. For a prime ` 6= p and i ∈ Z define P i ` := det(1− TF |H (Xk,Q`)) ∈ Q`[T ] and P i c,` := det(1− TF |H i c(Xk,Q`)) ∈ Q`[T ], where H (Xk,Q`) (resp. H i c(Xk,Q`)) denotes the étale cohomology of Xk (resp. compactly supported étale c...

In this paper we study the partially ordered set of endomorphism monoids of Rosenberg relations, which are used to characterize maximal clones on a finite set. The problem naturally splits into 49 cases of interrelationships of endomorphism monoids of Rosenberg relations. In order to make the paper self-contained, in addition to new results, we survey some previously published partial results p...

In this note, we prove that the endomorphism ring of a Kronecker module attached to a power series α ∈ k[[X]] is minimally generated by three generators, unless its degree d is less than 3. We prove this via the theory of algebraic curves, by proving that none of the affine curves arising from these endomorphism rings are planar for d ≥ 3, but can always be embedded in A3.