On σ -Twisted Functional Identities and Elementary Operators Over Division Rings

Open access Oct 2026

An Explicit Sextic Twist of a Supersingular Elliptic Curve in Characteristic Two

Let E:y2+y=x3+x over F2, a supersingular curve whose automorphism group is isomorphic to SL(2,3), of order twenty-four. Using an automorphism of order six, we construct the sextic twist of E along the fiber product of an Artin-Schreier and a Kummer covering, obtaining the family Z2+Z=B(t)X3+A(t)+c, in which the constan...

Guillermo Sosa-Gómez · Mathematics · 0 citations

Preprint Sep 2026

Moduli Spaces of Twisted Endomorphisms and Euler Characteristics

For a (quasi)projective variety $X$ and an automorphism $f$ of $X$, we define moduli spaces of twisted endomorphisms of sheaves on $X$. If the automorphism $f$ has finite order, we construct a sheaf of noncommutative algebras $\mathcal{A}_0(f)$ and show that sheaves with a twisted endomorphism can be described as $\mat...

Atharva Korde · 0 citations

Preprint Oct 2026

Cyclic automorphisms beyond the canonical bound

Let X be a smooth projective curve of genus g>= 2 over an algebraically closed field K, and suppose that Aut(X) contains a cyclic subgroup G of order N>2g - 2. The cases N>= 2g + 1 are known. We treat the two boundary values N = 2g and N = 2g - 1. In the tame case we obtain an explicit finite list of ramification signa...

A. Kazemifard, Saeed Tafazolian · 0 citations

Open access 2026

Directed graphs defined by prime divisors of polynomial values

Let L be the class of all nonconstant polynomials f(x) == Ax2 + Bx + C ∈ Z[x], which are not of the forms Ax2, Bx. We consider the directed graph Gf whose vertex set is P and p → q iff q | f(p), p ̸= q. Let Lf (p) be the set of simple directed paths starting at p and ℓf (p) = sup{|L| : L ∈ Lf (p)}, where |L| is the num...

I. Kátai, P. Bui · Annales Universitatis Scient... · 0 citations

Sep 2026

A remark on the automorphisms of the moduli space of logarithmic λ-connections over a curve

Abstract Let X be a compact Riemann surface of genus g ≥ 3 {g\geq 3} and let S be a finite subset of X. Let ξ be a fixed line bundle over X of degree d. We consider the moduli space ℳ Hod ⁢ ( X , S , ξ ) {\mathcal{M}_{\rm Hod}(X,S,\xi)} of logarithmic λ-connections singular over S ⊂ X {S\subset X} of rank n and degree...

Anoop Singh · Forum mathematicum · 0 citations

Preprint Oct 2026

Elliptic curves attached to Jacobians with imaginary multiplication

Let M be an imaginary quadratic field and A be an abelian variety of odd dimension g defined over Q for which there is a unitary algebra embedding of M in End^0(A_M) of signature ((g+1)/2,(g-1)/2). Extending a result by Fit\'e and Goodman, we show the existence of an elliptic curve E over Q with complex multiplication...

Francesc Fité, Francesc Pedret · 0 citations