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@article{MZM_2023_113_4_a13, author = {S. G. Tankeev}, title = {Hodge and {Mumford--Tate} groups of an {Abelian} {Variety,} {Complex} {Multiplication,} and {Frobenius} {Elements}}, journal = {Matemati\v{c}eskie zametki}, pages = {622--625}, publisher = {mathdoc}, volume = {113}, number = {4}, year = {2023}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_4_a13/} }
TY - JOUR AU - S. G. Tankeev TI - Hodge and Mumford--Tate groups of an Abelian Variety, Complex Multiplication, and Frobenius Elements JO - Matematičeskie zametki PY - 2023 SP - 622 EP - 625 VL - 113 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2023_113_4_a13/ LA - ru ID - MZM_2023_113_4_a13 ER -
S. G. Tankeev. Hodge and Mumford--Tate groups of an Abelian Variety, Complex Multiplication, and Frobenius Elements. Matematičeskie zametki, Tome 113 (2023) no. 4, pp. 622-625. http://geodesic.mathdoc.fr/item/MZM_2023_113_4_a13/
[1] B. B. Gordon, A Survey of the Hodge Conjecture, CRM Monograph Series, 10, ed. J. D. Lewis, Amer. Math. Soc., Providence, RI, 1999, 297–356 | MR
[2] B. Moonen, Notes on Mumford–Tate Groups, Centre Emile Borel, Paris, 1999
[3] J. Carlson, S. Müller-Stach, C. Peters, Period Mappings and Period Domains, Cambridge Stud. in Adv. Math., 168, Cambridge Univ. Press, Cambridge, 2018 | MR
[4] B. Moonen, An Introduction to Mumford–Tate Groups, 2004
[5] P. Deligne, Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Math., 900, Springer-Verlag, Berlin–New York, 1982, 9–100 | DOI | MR | Zbl
[6] D. Mumford, Abelian Varieties, Tata Institute of Fund. Research Stud. in Math., 5, Oxford University Press, London, 1970 | MR | Zbl
[7] S. Lang, Complex Multiplication, Springer-Verlag, New York, 1983 | MR | Zbl
[8] P. van Wamelen, Math. Comp., 68:225 (1999), 307–320 | DOI | MR
[9] G. Shimura, Yu. Taniyama, Complex Multiplication of Abelian Varieties and its Applications to Number Theory, Math. Soc. of Japan, Tokyo, 1961 | MR
[10] D. Mumford, Math. Ann., 181 (1969), 345–351 | DOI | MR
[11] G. Shimura, Abelian Varieties with Complex Multiplication and Modular Functions, Princeton Math. Ser., 46, Princeton Univ. Press, Princeton, NJ, 1988 | MR
[12] J.-P. Serre, J. Tate, Ann. of Math. (2), 88:3 (1968), 492–517 | DOI | MR
[13] I. I. Pyatetskii-Shapiro, Matem. sb., 85 (127):4 (8) (1971), 610–620 | MR | Zbl
[14] M. V. Borovoi, Voprosy teorii grupp i gomologicheskoi algebry, v. 1, Yaroslavskii gos. un-t, Yaroslavl, 1977, 3–53 | MR
[15] J.-P. Serre, Abelian $l$-adic Representations and Elliptic Curves, Benjamin, New York–Amsterdam, 1968 | MR
[16] Yu. Taniyama, J. Math. Soc. Japan, 9:3 (1957), 330–366 | DOI | MR
[17] J. S. Milne, Complex Multiplication, 2020 http://www.jmilne.org/math/CourseNotes/
[18] F. A. Bogomolov, C. R. Acad. Sci. Paris Ser. A-B, 290:15 (1980), 701–703 | MR
[19] W. Ch. Chi, Amer. J. Math., 114:2 (1992), 315–353 | DOI | MR
[20] J. Tate, Invent. Math., 2:2 (1966), 134–144 | DOI | MR
[21] J. Tate, Séminaire Bourbaki, v. 352, Lecture Notes in Math., 175, Springer, Berlin, 1971, 95–110 | MR