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


Author: Katrina Honigs; with an appendix by Jeffrey D. Achter; Sebastian Casalaina-Martin; Katrina Honigs; Charles Vial
Journal: Proc. Amer. Math. Soc. 146 (2018), 1005-1013
MSC (2010): Primary 14F05, 14K30; Secondary 14K02
DOI: https://doi.org/10.1090/proc/13810
Published electronically: October 25, 2017
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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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Additional Information

Katrina Honigs
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: honigs@math.utah.edu

Jeffrey D. Achter
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
Email: j.achter@colostate.edu

Sebastian Casalaina-Martin
Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309
Email: casa@math.colorado.edu

Charles Vial
Affiliation: Fakultät für Mathematik, Universität Bielefeld, P.O. Box 100 131, D-33 501 Bielefeld, Germany
Email: vial@math.uni-bielefeld.de

DOI: https://doi.org/10.1090/proc/13810
Received by editor(s): February 5, 2017
Received by editor(s) in revised form: May 5, 2017
Published electronically: October 25, 2017
Additional Notes: The author was partially supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship, Grant No. 1606268.
The second author was partially supported by grants from the the NSA (H98230-14-1-0161, H98230-15-1-0247 and H98230-16-1-0046)
The third author was partially supported by a Simons Foundation Collaboration Grant for Mathematicians (317572) and NSA grant H98230-16-1-0053.
The fourth author was supported by EPSRC Early Career Fellowship EP/K005545/1.
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 American Mathematical Society

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