Related papers: Birational isomorphisms between generalized Severi…

A conjecture of Amitsur states that two Severi-Brauer varieties are birationally isomorphic if and only if the underlying algebras are the same degree and generate the same cyclic subgroup of the Brauer group. It is known that generating…

Roquette proved Amitsur's conjecture for Severi-Brauer varieties associated with cyclic algebras using algebraic methods. We present a geometric proof of Roquette's result, providing simple and explicit birational isomorphisms.

We prove Amitsur's conjecture for Severi-Brauer varieties whose index is not a prime power.

In this paper we show that if two central simple $k$-algebras generate the same cyclic subgroup in $\mathrm{Br}(k)$, then there are rational maps between varieties associated to these algebras, such as Brauer--Severi varieties, norm…

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…

Let k be a field, and A a finite-dimensional k-algebra. Let d be an integer. Denote by Gr(d,A) the Grassmannian of d-subspaces of A (viewed as a k-vector space), and by GL_1(A) the algebraic k-group whose points are invertible elements of…

We consider central simple $K$-algebras which happen to bedifferential graded $K$-algebras. Two such algebras $A$ and $B$are considered equivalent if there are bounded complexes of finite dimensional$K$-vector spaces $C_A$ and $C_B$ such…

We define a generalization of the Brauer group $\operatorname{H}_\mathrm{B}^{n}(X)$ for an equi-dimensional scheme $X$ and $n>0$. In the case where $X$ is the spectrum of a local ring of a smooth algebra over a discrete valuation ring,…

By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a…

The generators of the group of birational automorphisms of any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to the projective plane are explicitly described.

We consider the set of forms of a toric variety over an arbitrary field: those varieties which become isomorphic to a toric variety after base field extension. In contrast to most previous work, we also consider arbitrary isomorphisms…

We prove that the only non-trivial finite subgroups of birational automorphism group of non-trivial Severi--Brauer surfaces over the field of rational numbers are~$\mathbb{Z}/3\mathbb{Z}$ and $(\mathbb{Z}/3\mathbb{Z})^2.$ Moreover, we show…

Let G be a semisimple affine algebraic group of inner type over a field F. We write C for the class of all finite direct products of projective G-homogeneous F-varieties. We determine the structure of the Chow motives with coefficients in a…

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…

Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial…

Biserial algebras are a classical class in the representation theory of algebras, generalizing Nakayama algebras. They were further generalized by Green and Schroll to multiserial algebras, which share many structural properties with…

Let ${\mathcal P}{\mathcal M}^\alpha_s$ be a moduli space of stable parabolic vector bundles of rank $n \geq 2$ and fixed determinant of degree $d$ over a compact connected Riemann surface $X$ of genus $g(X) \geq 2$. If $g(X) = 2$, then we…

Two semisimple algebraic groups of the same type are said to be motivic equivalent if the motives of the associated projective homogeneous varieties of the same type are isomorphic. We give general criteria of motivic equivalence in terms…

We introduce an analogue of the Novikov Conjecture on higher signatures in the context of the algebraic geometry of (nonsingular) complex projective varieties. This conjecture asserts that certain "higher Todd genera" are birational…

Let $\text{M}_C( 2, \mathcal{O}_C) \cong \mathbb{P}^3$ denote the coarse moduli space of semistable vector bundles of rank $2$ with trivial determinant over a smooth projective curve $C$ of genus $2$ over $\mathbb{C}$. Let $\beta_C$ denote…