Benjamin Church

collaborators

4 papers

math.AG2025

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

Benjamin Church

We construct a surface over $F_{p}$ with $I ¨ _{1}^{A ~ c ◯ t} (X) = 1$ that is supersingular -- in the sense that $H_{A ~ c ◯ t}^{2} (X, Q_{ℓ} (1))$ is spanned by algebra…

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

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

math.AG2024

Nowhere vanishing 1-forms on varieties admitting a good minimal model

Benjamin Church

We prove several conjectures relating the existence of nonvanishing 1- forms to smooth morphisms over abelian varieties, assuming the existence of good minimal models. The proof in…

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

Nowhere vanishing 1-forms on varieties admitting a good minimal model

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

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