Effective Convergence Bounds for Frobenius Structures on Connections
Elements of large order on varieties over prime finite fields
Let be a fixed algebraic variety defined by polynomials in variables with integer coefficients. We show that there exists a constant such that for almost all primes for all but at most points on the reduction of modulo at least one of the components has a large multiplicative order. This generalises several previous results and is a step towards a conjecture of B. Poonen.
Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini
Estimates for complete multiple exponential sums
Every ordinary symplectic isogeny class in positive characteristic is dense in the moduli.
Explicit bounds for split reductions of simple abelian varieties
Let be an absolutely simple abelian variety over a number field; we study whether the reductions tend to be simple, too. We show that if is a definite quaternion algebra, then the reduction is geometrically isogenous to the self-product of an absolutely simple abelian variety for in a set of positive density, while if is of Mumford type, then is simple for almost all . For a large class of abelian varieties with commutative absolute endomorphism ring, we give an explicit upper bound...