The theory of finite-dimensional division algebras witnessed several breakthroughs in the
latter decades of the twentieth century. Important advances, such as Amitsur's construction of …

This book introduces various notions defined in graded terms extending the notions most
frequently used as basic ingredients in the theory of Azumaya algebras: separability and …

Let $ X $ be a smooth scheme, $ Z $ a smooth closed subscheme, and $ U $ the open
complement. Given any localizing and $\mathbb {A}^ 1$-homotopy invariant of dg …

On the Brauer Group of Toric Varieties Page 1 TRANSACTIONS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 335, Number 2, February 1993 ON THE BRAUER GROUP …

We relate the Brauer group of a smooth variety over a-adic field to the geometry of the
special fibre of a regular model, using the purity theorem in étale cohomology. As an …

Toric varieties are a special class of rational varieties defined by equations of the form {\it
monomial= monomial}. For a good brief survey of the history and role of toric varieties see …

COMPUTING THE BRAUER-LONG GROUP OF Z/2 DIMODULE ALGEBRAS FR DeMEYER
TJ FORD In [ 131, Long introduced the group BD(R, G) of Page 1 Journal of Pure and …

If.!-',.... f. are irreducible polynomials in k [x,,.... x,], we wish to study the Brauer group of the
ring R= k [x,,.... x,][f', I,..... f,'1, where k is an algebraically closed field of characteristic p. The …

Publisher Summary This chapter focuses on the aspects of the Brauer group that are close
to the algebraic theory concerning the separable algebras representing the elements …

Let V be a reduced projective hypersurface in P ν and C the affine cone over V in X= A ν+ 1.
We employ cohomological methods to study the Brauer groups of the varieties C, C− P, X− C …