41 citations · 301 across the 36 of their papers we have counts for
41 papers
Fundamental group schemes of globally F-regular varieties
Charles Vial
We prove that every tower of connected quasi-torsor covers of a connected normal globally -regular projective variety over an algebraically closed field of positive characterist…
The Beauville-Voisin-Franchetta conjecture and LLSS eightfolds
Robert Laterveer, Charles Vial
The Chow rings of hyper-Kähler varieties are conjectured to have a particularly rich structure. In this paper, we formulate a conjecture that combines the Beauville-Voisin conjectu…
On proper splinters in positive characteristic
Johannes Krah, Charles Vial
While the splinter property is a local property for Noetherian schemes in characteristic zero, Bhatt observed that it imposes strong conditions on the global geometry of proper sch…
A complete answer to Albanese base change for incomplete varieties
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
Albanese varieties provide a standard tool in algebraic geometry for converting questions about varieties in general, to questions about Abelian varieties. A result of Serre provid…
Effective zero-cycles and the Bloch-Beilinson filtration
Olivier Martin, Charles Vial
A conjecture of Voisin states that two points on a smooth projective complex variety whose algebra of holomorphic forms is generated in degree 2 are rationally equivalent to each o…
De Rham-Betti classes with coefficients
Tobias Kreutz, Mingmin Shen, Charles Vial
Let and be algebraic extensions of the rational numbers inside the field of complex numbers. An -de Rham-Betti class on a smooth projective variety over is a cla…
The Walker Abel-Jacobi map descends
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
For a complex projective manifold, Walker has defined a regular homomorphism lifting Griffiths' Abel-Jacobi map on algebraically trivial cycle classes to a complex abelian variety,…
On the birational motive of hyper-Kähler varieties
Charles Vial
We introduce a new ascending filtration, that we call the co-radical filtration in analogy with the basic theory of co-algebras, on the Chow groups of pointed smooth projective var…
Cubic fourfolds, Kuznetsov components and Chow motives
Lie Fu, Charles Vial
We prove that the Chow motives of two smooth cubic fourfolds whose Kuznetsov components are Fourier-Mukai derived-equivalent are isomorphic as Frobenius algebra objects. As a corol…
Decomposition of the diagonal, intermediate Jacobians, and universal codimension-2 cycles in positive characteristic
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
We consider the connections among algebraic cycles, abelian varieties, and stable rationality of smooth projective varieties in positive characteristic. Recently Voisin constructed…
On the image of the second l-adic Bloch map
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
For a smooth projective geometrically uniruled threefold defined over a perfect field we show that there exists a canonical abelian variety over the field, namely the second algebr…
Zero-cycles on double EPW sextics
Robert Laterveer, Charles Vial
The Chow rings of hyperKähler varieties are conjectured to have a particularly rich structure. In this paper, we focus on the locally complete family of double EPW sextics and esta…
The generalized Franchetta conjecture for some hyper-Kähler varieties, II
Lie Fu, Robert Laterveer, Charles Vial
We prove the generalized Franchetta conjecture for the locally complete family of hyper-Kähler eightfolds constructed by Lehn-Lehn-Sorger-van Straten (LLSS). As a corollary, we est…
A functorial approach to regular homomorphisms
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
Classically, regular homomorphisms have been defined as a replacement for Abel--Jacobi maps for smooth varieties over an algebraically closed field. In this work, we interpret regu…
Multiplicative Chow-Künneth decompositions and varieties of cohomological K3 type
Lie Fu, Robert Laterveer, Charles Vial
Given a smooth projective variety, a Chow-Künneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin,…
A motivic global Torelli theorem for isogenous K3 surfaces
Lie Fu, Charles Vial
We prove that the Chow motives of twisted derived equivalent K3 surfaces are isomorphic, not only as Chow motives (due to Huybrechts), but also as Frobenius algebra objects. Combin…
Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of defi…
Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for abelian varieties
Charles Vial
We prove Bloch's conjecture for correspondences on powers of complex abelian varieties, that are "generically defined". As an application we establish vanishing results for (skew-)…
On the Chow ring of Cynk-Hulek Calabi-Yau varieties and Schreieder varieties
Robert Laterveer, Charles Vial
This note is about certain locally complete families of Calabi-Yau varieties constructed by Cynk and Hulek, and certain varieties constructed by Schreieder. We prove that the cycle…
Distinguished cycles on varieties with motive of abelian type and the Section Property
Lie Fu, Charles Vial
A remarkable result of Peter O'Sullivan asserts that the algebra epimorphism from the rational Chow ring of an abelian variety to its rational Chow ring modulo numerical equivalenc…
The generalized Franchetta conjecture for some hyper-Kähler varieties
Lie Fu, Robert Laterveer, Charles Vial +1
The generalized Franchetta conjecture for hyper-Kähler varieties predicts that an algebraic cycle on the universal family of certain polarized hyper-Kähler varieties is fiberwise r…
Derived equivalent threefolds, algebraic representatives, and the coniveau filtration
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
A conjecture of Orlov predicts that derived equivalent smooth projective varieties over a field have isomorphic Chow motives. The conjecture is known for curves, and was recently o…
Distinguished models of intermediate Jacobians
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
We show that the image of the Abel-Jacobi map admits functorially a model over the field of definition, with the property that the Abel-Jacobi map is equivariant with respect to th…
Parameter spaces for algebraic equivalence
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
A cycle is algebraically trivial if it can be exhibited as the difference of two fibers in a family of cycles parameterized by a smooth scheme. Over an algebraically closed field,…