On non-existence of full exceptional collections on some relative flags
Sa\v{s}a Novakovi\'c

TL;DR
This paper demonstrates that specific relative flag varieties lack full exceptional collections and explores their categorical representability, linking it to rational points and rationality over the base field.
Contribution
It establishes the non-existence of full exceptional collections on certain relative flags and connects categorical representability to rationality properties.
Findings
Certain relative flags cannot have full exceptional collections.
Categorical representability in dimension zero is equivalent to having a $k$-rational point.
Calculated categorical representability dimension for the studied flags.
Abstract
In this paper we show that certain relative flags cannot have full exceptional collections. We also prove that some of these flags are categorical representable in dimension zero if and only if they admit a full exceptional collection. As a consequence, these flags are categorical representable in dimension zero if and only if they have -rational points if and only if they are -rational. Moreover, we calculate the categorical representability dimension for the flags under consideration.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
