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.References
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Additional Information
- Katrina Honigs
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- MR Author ID: 1016722
- Email: honigs@math.utah.edu
- Jeffrey D. Achter
- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
- MR Author ID: 690384
- Email: j.achter@colostate.edu
- Sebastian Casalaina-Martin
- Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309
- MR Author ID: 754836
- 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
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1005-1013
- MSC (2010): Primary 14F05, 14K30; Secondary 14K02
- DOI: https://doi.org/10.1090/proc/13810
- MathSciNet review: 3750214