Hodge Classes and Abelian Varieties of Quaternionic Type

Giuseppe Lombardo

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 1, page 247-256
  • ISSN: 0392-4041

Abstract

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We obtain coniugacy classes (with respect to a 𝔰 ⁢ l 2 action) in the space of Hodge cycles in the middle cohomology of an Abelian variety of quaternionic type. The existence of such a class simplifies the study of the Hodge conjecture.

How to cite

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Lombardo, Giuseppe. "Hodge Classes and Abelian Varieties of Quaternionic Type." Bollettino dell'Unione Matematica Italiana 9-B.1 (2006): 247-256. <http://eudml.org/doc/289614>.

@article{Lombardo2006,
abstract = { We obtain coniugacy classes (with respect to a \(\mathfrak\{s\}l\_2\) action) in the space of Hodge cycles in the middle cohomology of an Abelian variety of quaternionic type. The existence of such a class simplifies the study of the Hodge conjecture.},
author = {Lombardo, Giuseppe},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {247-256},
publisher = {Unione Matematica Italiana},
title = {Hodge Classes and Abelian Varieties of Quaternionic Type},
url = {http://eudml.org/doc/289614},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Lombardo, Giuseppe
TI - Hodge Classes and Abelian Varieties of Quaternionic Type
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/2//
PB - Unione Matematica Italiana
VL - 9-B
IS - 1
SP - 247
EP - 256
AB - We obtain coniugacy classes (with respect to a \(\mathfrak{s}l_2\) action) in the space of Hodge cycles in the middle cohomology of an Abelian variety of quaternionic type. The existence of such a class simplifies the study of the Hodge conjecture.
LA - eng
UR - http://eudml.org/doc/289614
ER -

References

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  1. ABDULALI, S., Abelian varieities and the general Hodge conjecture, Compositio Math., 109, no. 3 (1997), 341-355. Zbl0891.14003
  2. FULTON, W. - HARRIS, J., Representation Theory, A first course, Graduate Texts in Mathematics, 129, Springer-Verlag, New York, (1991). Zbl0744.22001
  3. HERMANN, C. F., Some modular varieties related to P 4 , in: Abelian varieties (Egloffstein, 1993), de Gruyter, Berlin, (1995), 105-129. 
  4. LOMBARDO, G., Abelian varieties of Weil type and Kuga-Satake varieties, Tohoku Math. J, 53 (2001), 453-466. Zbl1081.14504
  5. VAN GEEMEN, B., Kuga-Satake varieties and the Hodge conjecture, in: The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), NATO Sci. Ser. C Math. Phys. Sci., 548, Kluwer Acad. Publ., Dordrecht (2000), 51-82. 
  6. VAN GEEMEN, B. - VERRA, A., Quaternionic Prym and Hodge classes, Topology, 42 (2003), 35-53. Zbl1074.14008

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