Benjamin Church

collaborators

3 papers

math.AG2025

Obstructions to unirationality for product-quotient surfaces over $F_{p}$

Benjamin Church

We construct a surface over $F_{p}$ with $π_{1}^{e ˊ t} (X) = 1$ that is supersingular -- in the sense that $H_{e ˊ t}^{2} (X, Q_{ℓ} (1))$ is spanned by algebraic…

math.AG2025

Nowhere vanishing 1-forms on 4-folds

Benjamin Church

In this note, we prove -- in dimension at most 4 -- a conjectue of Hao which says that a morphism $f : X \to A$ to a simple abelian variety $A$ is smooth if and only if there is a…

math.NT2024

$SL_{2}$ -character varieties of $2$ -generated groups and failure of weak integrality

Benjamin Church, Francisco García-Cortés

Let $ℓ$ be a prime number, $k$ a positive integer and consider the group $Γ_{ℓ^{k}} := ⟨ a, b ∣ a^{ℓ^{k} (ℓ^{k} - 1)} b a^{- ℓ^{k}} b^{- 2} ⟩$ . We prove that $Γ_{\ell…

Obstructions to unirationality for product-quotient surfaces over Fp​

Nowhere vanishing 1-forms on 4-folds

SL2​-character varieties of 2-generated groups and failure of weak integrality

Obstructions to unirationality for product-quotient surfaces over $F_{p}$

$SL_{2}$ -character varieties of $2$ -generated groups and failure of weak integrality