Derived equivalence, Albanese varieties, and the zeta functions of 3–dimensional varieties

Honigs, Katrina

doi:10.1090/proc/13810

Derived equivalence, Albanese varieties, and the zeta functions of $3$–dimensional varieties
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by Katrina Honigs; with an appendix by Jeffrey D. Achter; with an appendix by Sebastian Casalaina-Martin; with an appendix by Katrina Honigs; with an appendix by Charles Vial PDF

Proc. Amer. Math. Soc. 146 (2018), 1005-1013 Request permission

Abstract:

We show that any derived equivalent smooth, projective varieties of dimension $3$ over a finite field $\mathbb {F}_q$ have equal zeta functions. This result is an application of the extension to smooth, projective varieties over any field of Popa and Schnell’s proof that derived equivalent smooth, projective varieties over $\mathbb {C}$ have isogenous Albanese torsors; this result is proven in an appendix by Achter, Casalaina-Martin, Honigs and Vial.

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