Federico Scavia

activity

20152026

most citedThe behavior of essential dimension under specialization

5 citations · 16 across the 27 of their papers we have counts for

collaborators

34 papers

math.AG2026

The norm principle for extended Clifford groups

Federico Scavia

We prove the norm principle for the extended Clifford group $Ω (q)$ of every nondegenerate quadratic form $q$ of even dimension at least $4$ over an arbitrary field $F$ of character…

math.AG2026

Noether's problem for $A_{6}$ and $A_{7}$

Federico Scavia

We prove that $B_{k} A_{6}$ is stably rational over every field $k$ in which $2$ and $- 3$ are nonzero squares. Combining this with a theorem of Plans, we deduce that $B_{k} A_{7}$ is stably…

math.AG2026

Comb smoothing and local triviality of homogeneous spaces over a relative curve

Margot Bruneaux, Federico Scavia

Let $R$ be a Henselian local ring, let $κ$ be the residue field of $R$ , let $C$ be a smooth projective curve over $R$ with geometrically connected fibers, let $G$ be a reductive $C…

math.AG2026

Finite abelian subgroups of algebraic groups

Danny Ofek, Zinovy Reichstein, Federico Scavia

Let $k$ be an algebraically closed field, and let $G$ be an algebraic $k$ -group. We study finite abelian $k$ -subgroups $A \subset G$ whose order is not divisible by the characteris…

math.AG2026

Splitting Brauer classes by genus one curves over number fields

Benjamin Antieau, Asher Auel, Federico Scavia

We prove that every Severi-Brauer variety of dimension at least two over a number field contains a twisted elliptic normal curve. Consequently, every Brauer class over a number fie…

math.AG2026

Equivariant intermediate Jacobians and intersections of two quadrics

Federico Scavia

We present a short proof of the following theorem of Hassett and Tschinkel: for every finite group $G$ , a $G$ -equivariant smooth complete intersection of two quadrics in $\mathbb{P…

math.AG2026

Birational invariance of higher Amitsur groups

Federico Scavia, Yuri Tschinkel, Zhijia Zhang

Let $k$ be a field of characteristic zero and $G$ a finite group. We prove that for all $n \geq 2$ , the $n$ th Amitsur group is a stable $G$ -birational invariant of smooth projective…

math.AG2025

Brauer classes not split by genus one curves

Zinovy Reichstein, Federico Scavia

We show that there exist Brauer classes over a field $F$ which are not split by any genus one curve over $F$ . This answers a question of Clark and Saltman.

math.AG2025

On direct summands of products of Jacobians over arbitrary fields

Federico Scavia, Fumiaki Suzuki

We show that a principally polarized abelian variety over a field $k$ is, as an abelian variety, a direct summand of a product of Jacobians of curves which contain a $k$ -point if a…

math.AG2025

Specialization and rigidity

Zinovy Reichstein, Federico Scavia

We describe a general method, originated by Ofer Gabber, for showing that a very general fiber in a family has certain properties. We illustrate this method with concrete examples…

math.AG2025

Generically trivial torsors under constant groups

Alexis Bouthier, Kestutis Cesnavicius, Federico Scavia

We resolve the Grothendieck-Serre question over an arbitrary base field $k$ : for a smooth $k$ -group scheme $G$ and a smooth $k$ -variety $X$ , we show that every generically trivial…

math.NT2025

The lifting problem for Galois representations

Alexander Merkurjev, Federico Scavia

We solve the lifting problem for Galois representations in every dimension and in every characteristic. That is, we determine all pairs $(n, k)$ , where $n$ is a positive integer and…

math.NT2024

Galois representations modulo $p$ that do not lift modulo $p^{2}$

Alexander Merkurjev, Federico Scavia

For every finite group $H$ and every finite $H$ -module $A$ , we determine the subgroup of negligible classes in $H^{2} (H, A)$ , in the sense of Serre, over fields with enough roots of u…

math.NT2023★ 1 cited

Non-formality of Galois cohomology modulo all primes

Alexander Merkurjev, Federico Scavia

Let $p$ be a prime number and let $F$ be a field of characteristic different from $p$ . We prove that there exist a field extension $L / F$ and $a, b, c, d$ in $L^{\times}$ such that $(a…

math.NT2023★ 2 cited

On the Massey Vanishing Conjecture and Formal Hilbert 90

Alexander Merkurjev, Federico Scavia

Let $p$ be a prime number, let $G$ be a profinite group, let $θ : G \to Z_{p}^{\times}$ be a continuous character, and for all $n \geq 1$ write $\mathbb{Z}/p^n\mathbb{Z}(1…

math.AG2023

Varieties over $Q ˉ$ with infinite Chow groups modulo almost all primes

Federico Scavia

Let $E$ be the Fermat cubic curve over $Q ˉ$ . In 2002, Schoen proved that the group $C H^{2} (E^{3}) / ℓ$ is infinite for all primes $ℓ \equiv 1 (mod 3)$ . We show that $CH…

math.AG2023★ 1 cited

Two coniveau filtrations and algebraic equivalence over finite fields

Federico Scavia, Fumiaki Suzuki

We extend the basic theory of the coniveau and strong coniveau filtrations to the $ℓ$ -adic setting. By adapting the examples of Benoist--Ottem to the $ℓ$ -adic context, we sho…

math.NT2023★ 1 cited

The Massey Vanishing Conjecture for fourfold Massey products modulo 2

Alexander Merkurjev, Federico Scavia

We prove the Massey Vanishing Conjecture for $n = 4$ and $p = 2$ . That is, we show that for all fields $F$ , if a fourfold Massey product modulo $2$ is defined over $F$ , then it vanishe…

math.AG2022

Eilenberg-Moore spectral sequence and Hodge cohomology of classifying stacks

Dmitry Kubrak, Federico Scavia

Let $G$ be a smooth connected reductive group over a field $k$ and $Γ$ be a central subgroup of $G$ . We construct Eilenberg-Moore-type spectral sequences converging to the Hodge an…

math.AG2022

Quotient singularities in the Grothendieck ring of varieties

Louis Esser, Federico Scavia

Let $G$ be a finite group, $X$ be a smooth complex projective variety with a faithful $G$ -action, and $Y$ be a resolution of singularities of $X / G$ . Larsen and Lunts asked whether…

math.AG2022★ 2 cited

Non-algebraic geometrically trivial cohomology classes over finite fields

Federico Scavia, Fumiaki Suzuki

We give the first examples of smooth projective varieties $X$ over a finite field $F$ admitting a non-algebraic torsion $ℓ$ -adic cohomology class of degree $4$ which va…

math.AG2021

The behavior of essential dimension under specialization II

Zinovy Reichstein, Federico Scavia

Let $G$ be a linear algebraic group over a field. We show that, under mild assumptions, in a family of primitive generically free $G$ -varieties over a base variety $B$ the essentia…

math.AG2021★ 5 cited

The behavior of essential dimension under specialization

Zinovy Reichstein, Federico Scavia

Let $A$ be a discrete valuation ring with generic point $η$ and closed point $s$ . We show that in a family of torsors over $Spec (A)$ , the essential dimension of the…

math.AG2020

On the essential dimension of an algebraic group whose connected component is a torus

Zinovy Reichstein, Federico Scavia

Let $p$ be a prime integer, $k$ be a $p$ -closed field of characteristic $\neq = p$ , $T$ be a torus defined over $k$ , $F$ be a finite $p$ -group, and $1 \to T \to G \to F \to 1$ be an e…

The norm principle for extended Clifford groups

Noether's problem for A6​ and A7​

Comb smoothing and local triviality of homogeneous spaces over a relative curve

Finite abelian subgroups of algebraic groups

Splitting Brauer classes by genus one curves over number fields

Equivariant intermediate Jacobians and intersections of two quadrics

Birational invariance of higher Amitsur groups

Brauer classes not split by genus one curves

On direct summands of products of Jacobians over arbitrary fields

Specialization and rigidity

Generically trivial torsors under constant groups

The lifting problem for Galois representations

Galois representations modulo p that do not lift modulo p2

Non-formality of Galois cohomology modulo all primes

On the Massey Vanishing Conjecture and Formal Hilbert 90

Varieties over Qˉ​ with infinite Chow groups modulo almost all primes

Two coniveau filtrations and algebraic equivalence over finite fields

The Massey Vanishing Conjecture for fourfold Massey products modulo 2

Eilenberg-Moore spectral sequence and Hodge cohomology of classifying stacks

Quotient singularities in the Grothendieck ring of varieties

Non-algebraic geometrically trivial cohomology classes over finite fields

The behavior of essential dimension under specialization II

The behavior of essential dimension under specialization

On the essential dimension of an algebraic group whose connected component is a torus

Noether's problem for $A_{6}$ and $A_{7}$

Galois representations modulo $p$ that do not lift modulo $p^{2}$

Varieties over $Q ˉ$ with infinite Chow groups modulo almost all primes