Divyasree C-Ramachandran

arXiv2026

On the Vanishing of the Brauer-Manin Obstruction for Normic Bundles

We study the behaviour of the Brauer--Manin obstruction to the existence of rational points under finite field extensions. For $(p, mp)$-normic bundles over number fields, we prove that the Brauer--Manin obstruction vanishes after base change to finite extensions whose degrees satisfy suitable $p$-divisibility conditions depending on $m$. We further show that, for $(p,2p)$-normic bundles with $p=2$ or $3$, it is enough to assume that the extension degree is divisible by $p$. We also prove that the divisibility hypothesis is, in general optimal, by constructing a conic bundle for which the Brauer--Manin obstruction persists over a quadratic extension.

math.NT↗

arXiv2026

Zero cycles on Severi--Brauer flag varieties

Let $A$ be a central simple algebra over a field $F$ with index $n$ and let $\mathrm{SB}_r(A)$ denote the $r$-th generalized Severi--Brauer variety associated with $A$. We prove that the Chow group of zero cycles of degree zero $\mathrm{A_0}(\mathrm{SB}_r(A))$ is $(d, n/d)$-torsion where $d = (r,n)$. Our approach reduces the general case to division algebras of prime power index and yields several new instances in which $\mathrm{A_0}$ is trivial, together with sharper torsion bounds in general.\\ We also show that if $F$ is a local or global field, then $\mathrm{A_0}(\mathrm{SB}_r(A))=0$. Since Severi--Brauer flag varieties are stably birational to generalized Severi--Brauer varieties, these results extend to them, yielding corresponding torsion bounds and vanishing results for $\mathrm{A_0}(X)$, where $X$ is stably birational to $\mathrm{SB}_r(A)$.

math.AG↗