… genus gen(D) of a finite-dimensional central division algebra D over a field K as the set of
all classes [D ] in the Brauer group Br(K) that are represented by central division K-algebras D …

… For a finite-dimensional central simple algebra A … division algebra D of degree n over K,
one defines the genus gen(D) as the set of classes [D ] ∈ Br(K) represented by division algebras …

… In §4, we will give explicit estimates on the size of the genus of a quaternion algebra over
the field of rational functions of a split elliptic curve over a number field (cf. Theorem 4.1). Finally…

… Recently, Cecionit gave a further division algebra of order 16. It is here shown that the algebras
D … on the generality of our study of division algebras A. For, any A may be regarded as an …

… Thus the results on genus of division algebras from [11] and [17] rephrased in the language
of algebraic groups say that for any prime p, there exist fields over which there are inner …

… in the genus and show that we get better bounds on its … genus of the division algebra locally
in terms of the genus of its "unramified component" and the "ramified component". The genus …

… D is a central division F-algebra having the same maximal … , we construct a division algebra
of degree p with infinite genus. … x)-algebra Ci ramifies at the discrete valuation (trivial on K) of …

… This argument not only gives the finiteness of gen(D) but also provides a uniform bound
on its size over all division algebras D of a given degree n and a given number r of ramified …

… its ricg’of quotients is the generic division algebra D, n. Let K,,, … D is a divisor class of degree
d on C. Our main theorem (6.1.3) … Suppose that we are given an invertible sheaf L on S and …

… to Hasse's principle for fields of genus zero, and for genus 1 an example is given in [B8]. …
Finally, we describe the construction of a generic division algebra depending on a ground field …