Related papers: A geometric perspective on Amitsur's conjecture

We relate the Brauer group of a Kummer surface to the Brauer group of the corresponding abelian surface. For many pairs of elliptic curves over the rational numbers we prove that the Kummer surface attached to their product has trivial…

We show the existence of cluster $\mathcal{A}$-structures and cluster Poisson structures on any braid variety, for any simple Lie group. The construction is achieved via weave calculus and a tropicalization of Lusztig's coordinates. Several…

We investigate the Brauer class of the endomorphism algebra of the motive attached to a non-CM form. The ramification of the algebra is shown in many cases to be controlled by the normalized slopes of the form.

Let A and B be two central simple algebras of a prime degree n over a field F generating the same subgroup in the Brauer group. We show that the Chow motive of a Severi-Brauer variety SB(A) is a direct summand of the motive of a generalized…

We prove a conjecture of Fock and Goncharov which provides a birational equivalence of a cluster variety called the cluster symplectic double and a certain moduli space of local systems associated to a surface.

The Bloch-Beilinson-Murre conjectures predict the existence of a descending filtration on Chow groups of smooth projective varieties which is functorial with respect to the action of correspondences and whose graded parts depend solely on…

We introduce the notion of refined unramified cohomology of algebraic schemes and prove comparison theorems that identify some of these groups with cycle groups. This recovers for cycles of low codimensions on smooth projective varieties…

We study a natural birational invariant for varieties over finite fields and show that its vanishing on projective space is equivalent to the Tate conjecture, the Beilinson conjecture, and the Grothendieck--Serre semi-simplicity conjecture…

We formulate a categorification of Robertson's conjecture analogous to the categorical graph minor conjecture of Miyata--Proudfood--Ramos. We show that these conjectures imply the existence of a finite list of atomic graphs generating the…

In previous work, we established a duality between the algebraic de Rham cohomology of a flat algebraic connection on a smooth quasi-projective surface over the complex numbers and the rapid decay homology of the dual connection relying on…

We compute the cohomology ring of the complement of a toric arrangement with integer coefficients and investigate its dependency from the arrangement's combinatorial data. To this end, we study a morphism of spectral sequences associated to…

We extend a conjecture of Kimberley-Robertson on the abelianizations of certain square complex groups.

It was conjectured by Gorsky, Hogancamp, Mellit, and Nakagane that the left and right adjoints of the parabolic induction functor between homotopy categories of Soergel bimodules associated to a finite Coxeter group are related by the…

Let $\{P_i\}_{1 \leq i \leq r}$ and $\{Q_i\}_{1 \leq i \leq r}$ be two collections of Brauer Severi surfaces (resp. conics) over a field $k$. We show that the subgroup generated by the $P_i's$ in $Br(k)$ is the same as the subgroup…

Using an approach to the Jacobian Conjecture by L.M. Dru\.zkowski and K. Rusek 12], G. Gorni and G. Zampieri [19], and A.V. Yagzhev[27], we describe a correspondence between finite dimensional symmetric algebras and homogeneous tuples of…

The mixed area of a Reuleaux polygon and its symmetric with respect to the origin is expressed in terms of the mixed area of two explicit polygons. This gives a geometric explanation of a classical proof due to Chakerian. Mixed areas and…

We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.

We study the Brauer groups of regular conic bundles over elliptic curves defined over a number field $k$. We explicitly compute the Brauer group of the conic bundle when the singular fibres lie above $k$-points that are divisible by $2$ in…

We slightly extend a result of Oguiso on birational or automorphism groups (resp. of Lazi\'c - Peternell on Morrison-Kawamata cone conjecture) from Calabi-Yau manifolds of Picard number two to arbitrary singular varieties X (resp. to klt…

We define variants of PEL type of the Shimura varieties that appear in the context of the Arithmetic Gan-Gross-Prasad conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global and semi-global) integral…