Borys Kadets

activity

20182026

most citedLarge arboreal Galois representations

11 citations · 29 across the 12 of their papers we have counts for

collaborators

13 papers

math.NT2026

Generic Manin-Mumford

Lior Bary-Soroker, Borys Kadets

Given a collection of algebraic numbers $S \subset Q$ we study the varieties $V$ in $A_{C}^{m}$ such that $V(\mathbb{C})\cap\mathcal{S}^m…

math.NT2026

Hilbert irreducibility for algebraic points

Borys Kadets, Danny Neftin

We study the following problem: given a covering of curves $ϕ : X \to X_{0}$ over a number field $k$ , and an integer $d$ , when is the set \[\{p \in X_0(\overline{k})|\ \mathrm{de…

math.AG2025

Low degree subvarieties of universal hypersurfaces

Yifeng Huang, Borys Kadets, Olivier Martin

We study irreducible subvarieties of the universal hypersurface $X / B$ of degree $d$ and dimension $n$ . We prove that when $d$ is sufficiently large, a degree $k d$ subvari…

math.NT2024

Exponents of Jacobians and relative class groups

Borys Kadets, Daniel Keliher

We prove a lower bound for the exponent of the relative class group $Pic^{0} X_{1} / ϕ^{*} Pic^{0} X_{2}$ for a covering of curves $X_{1} \to X_{2}$ over a finite field $\mathbb{…

math.NT2022★ 3 cited

Subspace configurations and low degree points on curves

Borys Kadets, Isabel Vogt

This paper is devoted to understanding curves $X$ over a number field $k$ that possess infinitely many solutions in extensions of $k$ of degree at most $d$ ; such solutions are the…

math.NT2022

Galois specialization to symmetric points and the inverse Galois problem up to $S_{n}$

Borys Kadets

The paper is concerned with the following version of Hilbert's irreducibility theorem: if $π : X \to Y$ is a Galois $G$ -covering of varieties over a number field $k$ and $H \subset…

math.AG2021

Level structure, arithmetic representations, and noncommutative Siegel linearization

Borys Kadets, Daniel Litt

Let $ℓ$ be a prime, $k$ a finitely generated field of characteristic different from $ℓ$ , and $X$ a smooth geometrically connected curve over $k$ . Say a semisimple representat…

math.NT2020★ 2 cited

Odoni's conjecture on arboreal Galois representations is false

Philip Dittmann, Borys Kadets

Suppose $f \in K [x]$ is a polynomial. The absolute Galois group of $K$ acts on the preimage tree $T$ of $0$ under $f$ . The resulting homomorphism $ϕ_f: \mathrm{Gal}_K \to…

math.AG2020★ 2 cited

38406501359372282063949 & all that: Monodromy of Fano Problems

Sachi Hashimoto, Borys Kadets

A Fano problem is an enumerative problem of counting $r$ -dimensional linear subspaces on a complete intersection in $P^{n}$ over a field of arbitrary characteristic, wheneve…

math.NT2019

Estimates for the number of rational points on simple abelian varieties over finite fields

Borys Kadets

Let $A$ be a simple abelian variety of dimension $g$ over the field $F_{q}$ . The paper provides improvements on the Weil estimates for the size of $A (F_{q})$ . For an…

math.AG2018★ 7 cited

An arithmetic count of the lines meeting four lines in P^3

Padmavathi Srinivasan, Kirsten Wickelgren

We enrich the classical count that there are two complex lines meeting four lines in space to an equality of isomorphism classes of bilinear forms. For any field $k$ , this enrichme…

math.AG2018★ 4 cited

Sectional monodromy groups of projective curves

Borys Kadets

Fix a degree $d$ projective curve $X \subset P^{r}$ over an algebraically closed field $K$ . Let $U \subset (P^{r})^{*}$ be a dense open subvariety such that every hyper…

math.NT2018★ 11 cited

Large arboreal Galois representations

Borys Kadets

Given a field $K$ , a polynomial $f \in K [x]$ , and a suitable element $t \in K$ , the set of preimages of $t$ under the iterates $f^{\circ n}$ carries a natural structure of a $d$ -ar…

Generic Manin-Mumford

Hilbert irreducibility for algebraic points

Low degree subvarieties of universal hypersurfaces

Exponents of Jacobians and relative class groups

Subspace configurations and low degree points on curves

Galois specialization to symmetric points and the inverse Galois problem up to Sn​

Level structure, arithmetic representations, and noncommutative Siegel linearization

Odoni's conjecture on arboreal Galois representations is false

38406501359372282063949 & all that: Monodromy of Fano Problems

Estimates for the number of rational points on simple abelian varieties over finite fields

An arithmetic count of the lines meeting four lines in P^3

Sectional monodromy groups of projective curves

Large arboreal Galois representations

Galois specialization to symmetric points and the inverse Galois problem up to $S_{n}$