In this paper, we study and relate Calabi-Yau subHodge structures of Fano subvarieties of
different Grassmannians. In particular, we construct isomorphisms between Calabi-Yau …

Let C be an irreducible smooth complex projective curve of genus g≥ 2 and let Cd be its d-
fold symmetric product. In this paper, we study the question of semi-orthogonal …

This is the first of a series of papers, where we investigate hierarchies of generalized {L}\"{u}
roth problems on the hierarchy of rationality, starting with the obvious hierarchy between the …

We compute the algebraic K-theory of some classes of surfaces defined over finite fields. We
achieve this by first calculating the motivic cohomology groups and then studying the motivic …

Using the moduli space of semiorthogonal decompositions in a smooth projective family
introduced by the second, the third and the fourth author, we discuss indecomposability …

A fullness conjecture of Kuznetsov says that if a smooth projective variety $ X $ admits a full
exceptional collection of line bundles of length $ l $, then any exceptional collection of line …

In this paper we prove that a finite product of Brauer--Severi varieties is categorical
representable in dimension zero if and only if it admits a $ k $-rational point if and only if it is …

In this paper we show that the derived category of Brauer-Severi curves satisfies the Jordan-
H\" older property and cannot have quasi-phantoms, phantoms or universal phantoms. In …

We compute the algebraic $ K $-theory of some classes of surfaces defined over finite fields.
We achieve this by first calculating the motivic cohomology groups and then studying the …

A fundamental problem in mathematics is how to determine whether a given finite collection
of polynomials has a common solution, and how to quantify and qualify the shape of this …