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- W2607157053 abstract "In this paper we observe that for geometrically integral projective varieties $X$, admitting a full weak exceptional collection consisting of pure vector bundles, the existence of a $k$-rational point implies $mathrm{rdim}(X)=0$. We also study the symmetric power $S^n(X)$ of Brauer--Severi and involution varieties over $mathbb{R}$ and prove that the equivariant derived category $D^b_{S_n}(X^n)$ admits a full weak exceptional collection. As a consequence, we find $mathrm{rdim}(X)=0$ if and only if $mathrm{rdim}(D^b_{S_n}(X^n))=0$ for $1leq nleq 3$. If $X$ is Brauer--Severi, the existence of a $mathbb{R}$-rational point on $X$ or $S^3(X)$ is equivalent to $mathrm{rdim}(D^b_{S_3}(X^3))=0$." @default.
- W2607157053 created "2017-04-28" @default.
- W2607157053 creator A5026115226 @default.
- W2607157053 date "2017-04-08" @default.
- W2607157053 modified "2023-09-27" @default.
- W2607157053 title "Rational points on symmetric powers and categorical representability" @default.
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