arXiv subjects

Alice Lin

Publications and source records attributed to Alice Lin.

3 recordsLinked to original sources

arXiv2025

Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction

Using integral $p$-adic Hodge theory, Kato and Koshikawa define a generalization of the Faltings height of an abelian variety to motives defined over a number field. Assuming the adelic Mumford-Tate conjecture, we prove a finiteness property for heights in the isogeny class of a motive, where the isogenous motives are not required to be defined over the same number field. This expands on a result of Kisin and Mocz for the Faltings height in isogeny classes of abelian varieties.

math.NT↗

arXiv2024

Shafarevich's conjecture for families of hypersurfaces over function fields

Given a smooth quasi-projective complex algebraic variety $\mathcal{S}$, we prove that there are only finitely many Hodge-generic non-isotrivial families of smooth projective hypersurfaces over $\mathcal{S}$ of degree $d$ in $\mathbb{P}_{\mathbb C}^{n+1}$. We prove that the finiteness is uniform in $\mathcal{S}$ and we give examples where the result is sharp. We also prove similar results for certain complete intersections in $\mathbb{P}_{\mathbb C}^{n+1}$ of higher codimension and more generally for algebraic varieties whose moduli space admits a period map that satisfies the infinitesimal Torelli theorem.

math.AG↗

arXiv2019

Algebraic Relations Between Partition Functions and the $j$-Function

We obtain identities and relationships between the modular $j$-function, the generating functions for the classical partition function and the Andrews $spt$-function, and two functions related to unimodal sequences and a new partition statistic we call the "signed triangular weight" of a partition. These results follow from the closed formula we obtain for the Hecke action on a distinguished harmonic Maass form $\mathscr{M}(\tau)$ defined by Bringmann in her work on the Andrews $spt$-function. This formula involves a sequence of polynomials in $j(\tau)$, through which we ultimately arrive at expressions for the coefficients of the $j$-function purely in terms of these combinatorial quantities.

math.NT↗