High Frobenius Pushforwards Generate the Bounded Derived Category

Author(s)

• Matthew R. Ballard, University of South CarolinaFollow
• Srikanth B. Iyengar
• Pat Lank
• Alapan Mukhopadhyay
• Josh Pollitz

Document Type

Article

Abstract

This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme X of prime characteristic. The main result is that when the Frobenius map on X is finite, for any compact generator G of D(X) the Frobenius pushforward F^e_*G generates the bounded derived category whenever p^e is larger than the codepth of X, an invariant that is a measure of the singularity of X. The conclusion holds for all positive integers e when X is locally complete intersection. The question of when one can take G = O_X is also investigated. For smooth projective complete intersections it reduces to a question of generation of the Kuznetsov component.

Digital Object Identifier (DOI)

https://doi.org/10.1017/fms.2025.10156

Publication Info

Published in Forum of Mathematics, Sigma, Volume 14, 2026, pages e12-.

APA Citation

Ballard, M. R., Iyengar, S. B., Lank, P., Mukhopadhyay, A., & Pollitz, J. (2026). High Frobenius pushforwards generate the bounded derived category. Forum of Mathematics, Sigma, 14. https://doi.org/10.1017/fms.2025.10156

Rights

© The Author(s), 2026. Published by Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.