Let $S$ be a finitely generated domain with the field of fractions $F.$ Let X be a smooth,

geometrically connected affine variety over $S.$ Let $A$ be an Azumaya algebra over $X.$

Assume that for all large enough primes $p,$ $A_p$ splits over $X_p$-the reduction modulo $p$ of $X.$ Does this assumption imply that $A_{overline{F}}$ splits over $X_{overline{F}}?$ My naive guess is that the answer should be “yes”. Any suggestions or references would be

greatly appreciated.

# Tag: Brauer

## Brauer group of $mathbb{Z}_{(p)}$ – MathOverflow

Thanks for contributing an answer to MathOverflow!

- Please be sure to
*answer the question*. Provide details and share your research!

But *avoid* …

- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.

To learn more, see our tips on writing great answers.

## Brauer group of the Henselization

Let $R$ be a Noetherian local ring and let $R^h$ be its Henselization. What can we say about the kernel and range of the map

$$

Br(R) rightarrow Br(R^h)

$$

Are there interesting situations when the map is injective? Do we know more when $R$ is a discrete valuation ring?

## rt.representation theory – Non-isomorphic groups with same character tables and different Brauer character tables

Let $A$ be a discrete valuation ring with perfect residue field $k$ of characteristic $p$ and field of fractions $K$ of characteristic $0$. Let $G$ and $H$ be two finite groups and assume that $K$ is sufficiently large, so that the irreducible characters of both groups form a $K$-basis of the respective space of class functions with values in $K$.

If $G$ and $H$ have the same character table over $K$, i.e. if we have a bijection between the conjugacy classes of $G$ and $H$ and a bijection between the irreducible characters over $K$ under which the character table is preserved, do $G$ and $H$ then also have the same Brauer character table?

## Brauer Group of Projective Knot Curve

What is known about the brewer's group of a nodular curve with singularity as a common colon?