49 citations · 223 across the 37 of their papers we have counts for
7 papers · 1 filter
A heuristic for the distribution of point counts for random curves over a finite field
Jeffrey D. Achter, Daniel Erman, Kiran S. Kedlaya +2
How many rational points are there on a random algebraic curve of large genus over a given finite field ? We propose a heuristic for this question motivated by a…
On descending cohomology geometrically
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal…
The distribution of torsion subschemes of abelian varieties
Jeff Achter
We consider the distribution of p-power group schemes among the torsion of abelian varieties over finite fields of characteristic p, as follows. Fix natural numbers g and n, and le…
Local heuristics and an exact formula for abelian surfaces over finite fields
Jeff Achter, Cassie Williams
Consider a quartic -Weil polynomial . Motivated by equidistribution considerations we define, for each prime , a local factor which measures the relative frequency with…
Superspecial rank of supersingular abelian varieties and Jacobians
Jeff Achter, Rachel Pries
An abelian variety defined over an algebraically closed field k of positive characteristic is supersingular if it is isogenous to a product of supersingular elliptic curves and is…
Irreducibility of Newton strata in GU(1,n-1) Shimura varieties
Jeff Achter
Let L be a quadratic imaginary field, inert at the rational prime p. Fix an integer n at least 3, and let M be the moduli space (in characteristic p) of principally polarized abeli…