Applications of p-Adic Analysis for Bounding Periods of Subvarieties Under Etale Maps

Applications of p-Adic Analysis for Bounding Periods of Subvarieties Under Étale Maps

Using methods of p-adic analysis, we obtain effective bounds for the length of the orbit of a preperiodic subvariety Y⊂ X under the action of an étale endomorphism of X. As a corollary of our result, we obtain effective bounds for the size of torsion of any semiabelian variety over a finitely generated field of characteristic 0. Our method allows us to show that any finitely generated torsion s...

Bounding Periods of Subvarieties of (p)

Using methods of p-adic analysis, along with the powerful result of Medvedev-Scanlon [MS14] for the classification of periodic subvarieties of (P1)n, we bound the length of the orbit of a periodic subvariety Y ⊂ (P1)n under the action of a dominant endomorphism.

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

Irrationality of Certain p - adic Periods for Small p

Apéry’s proof [13] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significant new results (although further progress has been made on the irrationality of zeta values [1, 14]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and Lege...

Bounding slopes of p-adic modular forms

Let p be prime, N be a positive integer prime to p, and k be an integer. Let Pk(t) be the characteristic series for Atkin’s U operator as an endomorphism of p-adic overconvergent modular forms of tame level N and weight k. Motivated by conjectures of Gouvêa and Mazur, we strengthen a congruence in [W] between coefficients of Pk and Pk′ for k ′ p-adically close to k. For p − 1 | 12, N = 1, k = 0...