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On the irreducibility of the hyperplane sections of Fermat varieties in $\mathbb{P}^3$ in characteristic $2$
Splitting of abelian varieties
1. | Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Canada M5S 2E4, Canada, Canada |
References:
[1] |
F. Bogomolov, Sur l'algébricité des représentations $l$-adiques, Comptes Rendus Acad. Sci. Paris, 290 (1980), 701-703. |
[2] |
N. Bourbaki, Groupes et Algèbres de Lie, Hermann, Paris, 1975. |
[3] |
C.-L. Chai and F. Oort, A note on the existence of absolutely simple Jacobians, J. Pure Appl. Algebra, 155 (2001), 115-120.
doi: 10.1016/S0022-4049(99)00096-1. |
[4] |
A. Cojocaru, Reductions of an elliptic curve with almost prime orders, Acta Arith., 119 (2005), 265-289.
doi: 10.4064/aa119-3-3. |
[5] |
C. David and J. Wu, Almost prime values of the order of elliptic curves over finite fields, Forum Math., 24 (2012), 99-119.
doi: 10.1515/form.2011.051. |
[6] |
P. Deligne, Variétés de Shimura: Interprétation modulaire, et techniques de construction de modèles canoniques, in Proc. Symp. Pure Math. (eds. A. Borel and W. Casselman), AMS, Providence, 1979, 247-289. |
[7] |
G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math., 73(1983), 349-366.
doi: 10.1007/BF01388432. |
[8] |
A. Grothendieck, Revêtements étales et Groupe Fondamental, Springer, Berlin, 1971. |
[9] |
N. Katz, Galois properties of torsion points of abelian varieties, Invent. Math., 62 (1981), 481-502.
doi: 10.1007/BF01394256. |
[10] |
N. Koblitz, Primality of the number of points on an elliptic curve over a finite field, Pacific J. Math., 131 (1988),157-165.
doi: 10.2140/pjm.1988.131.157. |
[11] |
S. A. Miri and V. Kumar Murty, An application of sieve methods to elliptic curves, in INDOCRYPT 2001, Springer, Berlin, 2001, 91-98.
doi: 10.1007/3-540-45311-3_9. |
[12] |
V. Kumar Murty, The least prime which does not split completely, Forum Math., 6 (1994), 555-565.
doi: 10.1515/form.1994.6.555. |
[13] |
V. Kumar Murty and V. Patankar, Splitting of abelian varieties, Intl. Math. Res. Notices, 12 (2008), Article ID rnn 033, 27 pp.
doi: 10.1093/imrn/rnn033. |
[14] |
V. Kumar Murty and Y. Zong, Splitting of abelian varieties, elliptic minuscule pairs,, preprint, ().
|
[15] |
M. Ram Murty, On Artin's conjecture, J. Number Theory, 16 (1983), 147-168.
doi: 10.1016/0022-314X(83)90039-2. |
[16] |
M. Ram Murty, Artin's conjecture and elliptic analogues, in Sieve methods, exponential sums, and their applications in number theory (eds. G.R.H. Greaves, G. Harman and M.N. Huxley), Cambridge Univ. Press, Cambridge, 1996, 325-344.
doi: 10.1017/CBO9780511526091.022. |
[17] |
J. Tate, Classes d'isogénie de variétés abéliennes sur un corps fini (d'après T.Honda), in Séminaire Bourbaki, Springer, Heidelberg, 1971, 95-110. |
[18] |
J. Tits, Classification of algebraic semisimple groups, in Proc. Sympos. Pure Math. (eds. A. Borel and G. Mostow), AMS, Providence, 1966, 33-62. |
[19] |
J.-J. Urroz, Almost prime order of CM elliptic cures modulo $p$, in Algorithmic Number Theory, Springer, Berlin, 2008, 74-87.
doi: 10.1007/978-3-540-79456-1_4. |
show all references
References:
[1] |
F. Bogomolov, Sur l'algébricité des représentations $l$-adiques, Comptes Rendus Acad. Sci. Paris, 290 (1980), 701-703. |
[2] |
N. Bourbaki, Groupes et Algèbres de Lie, Hermann, Paris, 1975. |
[3] |
C.-L. Chai and F. Oort, A note on the existence of absolutely simple Jacobians, J. Pure Appl. Algebra, 155 (2001), 115-120.
doi: 10.1016/S0022-4049(99)00096-1. |
[4] |
A. Cojocaru, Reductions of an elliptic curve with almost prime orders, Acta Arith., 119 (2005), 265-289.
doi: 10.4064/aa119-3-3. |
[5] |
C. David and J. Wu, Almost prime values of the order of elliptic curves over finite fields, Forum Math., 24 (2012), 99-119.
doi: 10.1515/form.2011.051. |
[6] |
P. Deligne, Variétés de Shimura: Interprétation modulaire, et techniques de construction de modèles canoniques, in Proc. Symp. Pure Math. (eds. A. Borel and W. Casselman), AMS, Providence, 1979, 247-289. |
[7] |
G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math., 73(1983), 349-366.
doi: 10.1007/BF01388432. |
[8] |
A. Grothendieck, Revêtements étales et Groupe Fondamental, Springer, Berlin, 1971. |
[9] |
N. Katz, Galois properties of torsion points of abelian varieties, Invent. Math., 62 (1981), 481-502.
doi: 10.1007/BF01394256. |
[10] |
N. Koblitz, Primality of the number of points on an elliptic curve over a finite field, Pacific J. Math., 131 (1988),157-165.
doi: 10.2140/pjm.1988.131.157. |
[11] |
S. A. Miri and V. Kumar Murty, An application of sieve methods to elliptic curves, in INDOCRYPT 2001, Springer, Berlin, 2001, 91-98.
doi: 10.1007/3-540-45311-3_9. |
[12] |
V. Kumar Murty, The least prime which does not split completely, Forum Math., 6 (1994), 555-565.
doi: 10.1515/form.1994.6.555. |
[13] |
V. Kumar Murty and V. Patankar, Splitting of abelian varieties, Intl. Math. Res. Notices, 12 (2008), Article ID rnn 033, 27 pp.
doi: 10.1093/imrn/rnn033. |
[14] |
V. Kumar Murty and Y. Zong, Splitting of abelian varieties, elliptic minuscule pairs,, preprint, ().
|
[15] |
M. Ram Murty, On Artin's conjecture, J. Number Theory, 16 (1983), 147-168.
doi: 10.1016/0022-314X(83)90039-2. |
[16] |
M. Ram Murty, Artin's conjecture and elliptic analogues, in Sieve methods, exponential sums, and their applications in number theory (eds. G.R.H. Greaves, G. Harman and M.N. Huxley), Cambridge Univ. Press, Cambridge, 1996, 325-344.
doi: 10.1017/CBO9780511526091.022. |
[17] |
J. Tate, Classes d'isogénie de variétés abéliennes sur un corps fini (d'après T.Honda), in Séminaire Bourbaki, Springer, Heidelberg, 1971, 95-110. |
[18] |
J. Tits, Classification of algebraic semisimple groups, in Proc. Sympos. Pure Math. (eds. A. Borel and G. Mostow), AMS, Providence, 1966, 33-62. |
[19] |
J.-J. Urroz, Almost prime order of CM elliptic cures modulo $p$, in Algorithmic Number Theory, Springer, Berlin, 2008, 74-87.
doi: 10.1007/978-3-540-79456-1_4. |
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