Jeff Achter

activity

20242026

collaborators

5 papers

math.NT2026

On the pointwise convergence of the number of abelian varieties over $F_{p}$ with fixed trace

Zhao Yu Ma, Jit Wu Yap, Jeff Achter +1

Extending Katz-Sarnak heuristics, Ballini-Lombardo-Verzobio [BLV25] conjectures a limiting distribution as $p \to \infty$ for $# A_{g} (F_{p}, t)$ , the number of $g$ -dimensional…

math.AG2025

Regular homomorphisms, with a twist

Jeff Achter, Sebastian Casalaina-Martin, Charles Vial

Let $X / K$ be a variety over a field, and $A / K$ an abelian variety. A regular homomorphism to $A$ (in codimension $i$ ) induces, for every smooth geometrically connected pointed $K$ -…

math.AG2025

Decomposition of the diagonal, intermediate Jacobians, and universal codimension-2 cycles in positive characteristic

Jeff Achter, Sebastian Casalaina-Martin, Charles Vial

We consider the connections among algebraic cycles, abelian varieties, and stable rationality of smooth projective varieties in positive characteristic. Recently Voisin constructed…

math.AG2024

Putting the p back in Prym

Jeff Achter, Sebastian Casalaina-Martin

After Jacobians of curves, Prym varieties are perhaps the next most studied abelian varieties. They turn out to be quite useful in a number of contexts. For technical reasons, ther…

math.AG2024

Images of abelian schemes

Jeff Achter, Sebastian Casalaina-Martin, Jonathan Wise

We provide some conditions for the image of a morphism of abelian schemes to again be an abelian scheme. For context, in characteristic 0, the image is always an abelian scheme; in…