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The $a$-number of jacobians of certain maximal curves | ||
| Transactions on Combinatorics | ||
| دوره 10، شماره 2، شهریور 2021، صفحه 121-128 اصل مقاله (234.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2021.124678.1758 | ||
| نویسندگان | ||
| vahid Nourozi1؛ Saeed Tafazolian* 2؛ Farhad Rahamti1 | ||
| 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 | ||
| In this paper, we compute a formula for the $a$-number of certain maximal curves given by the equation $y^{q}+y=x^{\frac{q+1}{2}}$ over the finite field $\mathbb{F}_{q^2}$. The same problem is studied for the maximal curve corresponding to $\sum_{t=1}^s y^{q/2^t}=x^{q+1}$ with $q=2^s$, over the finite field $\mathbb{F}_{q^2}$. | ||
| کلیدواژه‌ها | ||
| $a$-number؛ Cartier operator؛ Super-singular Curves؛ Maximal Curves | ||
| مراجع | ||
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[1] M. Abdon and F. Torres, On maximal curves in characteristic two, Manuscripta Math., 99 (1999) 39–53.
[2] P. Cartier, Une nouvelle opration sur les formes diffrentielles. C. R. Acad. Sci. Paris, 244 (1957) 426–428.
[3] P. Cartier, Questions de rationalit des diviseurs en gomtrie algbrique, Bull. Soc. Math. France, 86 (1958) 177–251.
[4] D. Gorenstein, An arithmetic theory of adjoint plane curves, Trans. Am. Math. Soc., 72 (1952) 414–436.
[5] R. Fuhrmann, A. Garcia and F. Torres, On maximal curves, J. Number Theory, 67 (1997) 29–51.
[6] R. Fuhrmann and F. Torres, The genus of curves over finite fields with many rational points, Manuscripta Math, 89 (1996) 103–106. [7] H. Friedlander, D. Garton, B. Malmskog, R. Pries and C. Weir, The a-number of Jacobians of Suzuki curves, Proc. Amer. Math. Soc., 141 (2013) 3019–3028. [8] J. Gonzlez, Hasse-Witt matrices for the Fermat curves of prime degree, Tohoku Math. J., 49 (1997) 149–163.
[9] B. H. Gross, Group representations and lattices, J. Am. Math. Soc., 3 (1990) 929–960.
[10] Y. Ihara, Some remarks on the number of rational points of algebraic curves over finite fields, J. Fac. Sci. Tokyo, 28 (1981) 721–724. [11] T. Kodama and T. Washio, Hasse-Witt matrices of Fermat curves, Manuscr. Math., 60 (1988) 185–195.
[12] K.-Z. Li and F. Oort, Moduli of Supersingular Abelian Varieties, Lecture Notes in Mathematics, 1680, Springer- Verlag, Berlin, 1998, iv+116pp. [13] M. Montanucci and P. Speziali, The a-numbers of Fermat and Hurwitz curves, J. Pure Appl. Algebra, 222 (2018) 477–488. [14] V. Nourozi, F. Rahmati and S. Tafazolian, The a-number of certain hyperelliptic curves, ArXiv: 1902.03672v2, 2019. [15] R. Pries and C. Weir, The Ekedahl-Oort type of Jacobians of Hermitian curves, Asian J. Math., 19 (2015) 845–869.
[16] H. G. Rück and H. Stichtenoth, A characterization of Hermitian function fields over finite fields, J. Reine Angew. Math., 457 (1994) 185–188. [17] C. S. Seshadri, Loperation de Cartier, Applications, In Varietes de Picard, 4, of Sminaire Claude Chevalley. Secrtariat Mathmatiques, Paris, 1958–1959. [18] M. Tsfasman, S. Vladut and D. Nogin, Algebraic geometric codes: basic notions, 139, of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2007. [19] N. Yui, On the Jacobian Varieties of Hyperelliptic Curves over Fields of Characteristic p, J. Algebra, 52 (1978) 378–410. | ||
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