Benjamin Bakker

collaborators

6 papers

math.AG2026

Deformations of fibered Calabi--Yau varieties

Benjamin Bakker, Kristin DeVleming, Stefano Filipazzi +5

KollÃ¡r showed that small deformations of elliptically fibered smooth $K$ -torsion varieties with $H^{2} (X, O_{X}) = 0$ remain elliptically fibered. We extend this result to any…

math.NT2026

$p$ -adic hyperbolicity for Shimura varieties and period images

Benjamin Bakker, Abhishek Oswal, Ananth N. Shankar +1

We prove that Shimura varieties and geometric period images satisfy a $p$ -adic extension property for large enough primes $p$ . More precisely, let $\mathsf{D}^{\times}\subset \math…

math.AG2026

Non-abelian Hodge theory for non-proper varieties and the linear Shafarevich conjecture

Benjamin Bakker

We survey recent advances in non-abelian Hodge theory in the "mixed" setting of non-proper algebraic varieties. We then describe how these tools are used to construct algebraic Sha…

math.AG2025

Baily--Borel compactifications of period images and the b-semiampleness conjecture

Benjamin Bakker, Stefano Filipazzi, Mirko Mauri +1

We address two questions related to the semiampleness of line bundles arising from Hodge theory. First, we prove there is a functorial compactification of the image of a period map…

math.NT2025

Finiteness of function field-valued points on exceptional Shimura varieties

Benjamin Bakker, Ananth N. Shankar, Jacob Tsimerman

Let $C / k$ be a smooth curve over a finite field of characteristic $p > 0$ . We prove that there are finitely many principally polarized abelian schemes of given dimension $g$ over $C$ …

math.NT2025

Integral canonical models of exceptional Shimura varieties

Benjamin Bakker, Ananth N Shankar, Jacob Tsimerman

We prove that Shimura varieties admit integral canonical models for sufficiently large primes. In the case of abelian-type Shimura varieties, this recovers work of Kisin-Kottwitz f…