The $a$-numbers of Jacobians of Suzuki curves
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- by Holley Friedlander, Derek Garton, Beth Malmskog, Rachel Pries and Colin Weir PDF
- Proc. Amer. Math. Soc. 141 (2013), 3019-3028 Request permission
Abstract:
For $m \in {\mathbb N}$, let $S_m$ be the Suzuki curve defined over $\mathbb {F}_{2^{2m+1}}$. It is well-known that $S_m$ is supersingular, but the $p$-torsion group scheme of its Jacobian is not known. The $a$-number is an invariant of the isomorphism class of the $p$-torsion group scheme. In this paper, we compute a closed formula for the $a$-number of $S_m$ using the action of the Cartier operator on $H^0(S_m,\Omega ^1)$.References
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Additional Information
- Holley Friedlander
- Affiliation: Department of Mathematics, University of Massachusetts–Amherst, Amherst, Massachusetts 01003
- Email: holleyf@math.umass.edu
- Derek Garton
- Affiliation: Department of Mathematics, University of Wisconsin–Madison, Madison, Wisconsin 53706
- Address at time of publication: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
- Email: garton@math.wisc.edu
- Beth Malmskog
- Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06457
- Address at time of publication: Department of Mathematics and Statistics, Colorado College, Colorado Springs, Colorado 80946
- MR Author ID: 897266
- Email: emalmskog@wesleyan.edu
- Rachel Pries
- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80521
- MR Author ID: 665775
- Email: pries@math.colostate.edu
- Colin Weir
- Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada T2N 1N4
- MR Author ID: 1024772
- Email: cjweir@ucalgary.ca
- Received by editor(s): November 2, 2011
- Received by editor(s) in revised form: November 29, 2011
- Published electronically: May 31, 2013
- Additional Notes: The third author was partially supported by NSF grant DMS-11-01712
- Communicated by: Matthew A. Papanikolas
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 141 (2013), 3019-3028
- MSC (2010): Primary 11G20, 14H40; Secondary 14G50
- DOI: https://doi.org/10.1090/S0002-9939-2013-11581-9
- MathSciNet review: 3068955