ALGEBRAIC CYCLES AND TATE CLASSES ON HILBERT MODULAR VARIETIES
2014 ◽
Vol 10
(01)
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pp. 161-176
Keyword(s):
Rank One
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Let E/ℚ be a totally real number field that is Galois over ℚ, and let π be a cuspidal, nondihedral automorphic representation of GL 2(𝔸E) that is in the lowest weight discrete series at every real place of E. The representation π cuts out a "motive" M ét (π∞) from the ℓ-adic middle degree intersection cohomology of an appropriate Hilbert modular variety. If ℓ is sufficiently large in a sense that depends on π we compute the dimension of the space of Tate classes in M ét (π∞). Moreover if the space of Tate classes on this motive over all finite abelian extensions k/E is at most of rank one as a Hecke module, we prove that the space of Tate classes in M ét (π∞) is spanned by algebraic cycles.
2017 ◽
Vol 153
(9)
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pp. 1769-1778
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Keyword(s):
Keyword(s):
2009 ◽
Vol 145
(5)
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pp. 1114-1146
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1981 ◽
Vol 1981
(324)
◽
pp. 192-210
1991 ◽
Vol 37
(3)
◽
pp. 343-365
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Keyword(s):
Keyword(s):