Titlebook: Arithmetic Geometry, Number Theory, and Computation; Jennifer S. Balakrishnan,Noam Elkies,John Voight Conference proceedings 2021 The Edit

启发

chemical-peel

expire

Elliptic Curves with Good Reduction Outside of the First Six Primes,e computation time to conclude. We present data on the distribution of various quantities associated to curves in the set. We also discuss the connection to .-unit equations and the existence of rational elliptic curves with maximal conductor.

FLAG

Project

Restrictions on Weil Polynomials of Jacobians of Hyperelliptic Curves, particular form modulo 2. For fixed . ≥ 1, the proportion of isogeny classes of .-dimensional abelian varieties defined over . which fail this condition is 1 − .(2. + 2)∕2. as . →. ranges over odd prime powers, where .(.) denotes the number of partitions of . into odd parts.

GREG

Effective Obstruction to Lifting Tate Classes from Positive Characteristic,ur method relies only on a single prime reduction and gives the possibility of cutting down on the dimension of Tate classes by two or more. The obstruction map comes from .-adic variational Hodge conjecture and we rely on the recent advancement by Bloch–Esnault–Kerz to interpret our bounds.

constellation

Conjecture: 100% of Elliptic Surfaces Over , have Rank Zero,tify this conjecture. We then discuss how it would follow from either understanding of certain .-functions, or from understanding of the local behaviour of the surfaces. Finally, we make a conjecture about ranks of elliptic surfaces over finite fields, and highlight some experimental evidence supporting it.

Medley

A Robust Implementation for Solving the ,-Unit Equation and Several Applications,rove an asymptotic version of Fermat’s Last Theorem for totally real cubic number fields with bounded discriminant where 2 is totally ramified. In addition, we use the implementation to find all solutions to some cubic Ramanujan-Nagell equations.

Fortify

charisma

Conference proceedings 2021ite fields. The articles also explore examples important for future research..Specific topics include.● algebraic varieties over finite fields.● the Chabauty-Coleman method.● modular forms.● rational points on curves of small genus.● S-unit equations and integral points..