Federico Scavia

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…

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…

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…

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…

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…

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…

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…

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.

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…

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…

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.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.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…

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…

On the Mixed Tate property and the motivic class of the classifying stack of a finite group

Federico Scavia

Let $G$ be a finite group, and let ${B_{C} G}$ the class of its classifying stack $B_{C} G$ in Ekedahl's Grothendieck ring of algebraic $C$ -stacks $K_0(\…

Motivic classes of classifying stacks of finite groups and unramified cohomology

Federico Scavia

Combining work of Peyre, Colliot-Thélène and Voisin, we give the first example of a finite group $G$ such that the motivic class of its classifying stack $B G$ in Ekedahl's Grothend…