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The $a$-number of maximal curves of third largest genus | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 2، دوره 3، شماره 1، اردیبهشت 2022، صفحه 11-16 اصل مقاله (353.49 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.20511.1069 | ||
| نویسندگان | ||
| Vahid Nourozi1؛ Saeed Tafazolian* 2 | ||
| 1Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran | ||
| 2IMECC/UNICAMP, R. Sergio Buarque de Holanda, 651, Cidade Universitaria, Zeferino Vaz, 13083-859, Campinas, SP, Brazil | ||
| چکیده | ||
| 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 $y^q + y = x^{\frac{q+1}{3}}$ and $\sum_{t=1}^{s} y^{q/3^t}= x^{q+1}$ with $q = 3^s$ over the finite field $\mathbb{F}_{q^2}$ using the action of the Cartier operator on $H^0(\mathcal{C},\Omega^1)$. | ||
| کلیدواژه‌ها | ||
| $a$-number؛ Cartier operator؛ Super-singular curves؛ Maximal curves | ||
| مراجع | ||
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[1] P. Cartier, Une nouvelle op´eration sur les formes diff´erentielles, C. R. Acad. Sci. Paris, 244 (1957), pp. 426– 428.
[2]__ , Questions de rationalit´e des diviseurs en g´eom´etrie alg´ebrique, Bull. Soc. Math. France, 86 (1958), pp. 177–251.
[3] J. Gonzalez, Hasse-Witt matrices for the Fermat curves of prime degree, Tohoku Math. J. (2), 49 (1997), pp. 149–163.
[4] D. Gorenstein, An arithmetic theory of adjoint plane curves, Trans. Amer. Math. Soc., 72 (1952), pp. 414– 436.
[5] J. W. P. Hirschfeld, G. Korchmaros, and F. Torres, Algebraic curves over a finite field, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, 2008.
[6] T. Kodama and T. Washio, Hasse-Witt matrices of Fermat curves, Manuscripta Math., 60 (1988), pp. 185– 195.
[7] M. Montanucci and P. Speziali, The a-numbers of Fermat and Hurwitz curves, J. Pure Appl. Algebra, 222 (2018), pp. 477–488.
[8] V. Nourozi, F. Rahmati, and S. Tafazolian, The a-number of certain hyperelliptic curves, arXiv preprint arXiv:1902.03672, (2019).
[9] V. Nourozi, S. Tafazolian, and F. Rahmati, The a-number of Jacobians of certain maximal curves, Trans. Comb., 10 (2021), pp. 121–128.
[10] R. Pries and C. Weir, The Ekedahl-Oort type of Jacobians of Hermitian curves, Asian J. Math., 19 (2015), pp. 845–869.
[11] C. S. Seshadri, L’op´eration de Cartier. Applications, S´eminaire Claude Chevalley, 4 (1958-1959), pp. 1–26. talk:6.
[12] M. Tsfasman, S. Vladut¸, and D. Nogin , Algebraic geometric codes: basic notions, vol. 139 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2007.
[13] N. Yui, On the Jacobian varieties of hyperelliptic curves over fields of characteristic p > 2, J. Algebra, 52 (1978), pp. 378–410. | ||
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