A theorem of Matsushima
1974 ◽
Vol 54
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pp. 123-134
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Keyword(s):
In [7], Matsushima studied the vector bundles over a complex torus. One of his main theorems is: A vector bundle over a complex torus has a connection if and only if it is homogeneous (Theorem (2.3)). The aim of this paper is to prove the characteristic p > 0 version of this theorem. However in the characteristic p > 0 case, for any vector bundle E over a scheme defined over a field k with char, k = p, the pull back F*E of E by the Frobenius endomorphism F has a connection. Hence we have to replace the connection by the stratification (cf. (2.1.1)). Our theorem states: Let A be an abelian variety whose p-rank is equal to the dimension of A. Then a vector bundle over A has a stratification if and only if it is homogeneous (Theorem (2.5)).
Keyword(s):
1976 ◽
Vol 61
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pp. 197-202
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Keyword(s):
Keyword(s):
2011 ◽
Vol 84
(2)
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pp. 255-260
2012 ◽
Vol 10
(2)
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pp. 299-369
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Keyword(s):
1982 ◽
Vol 271
(1)
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pp. 117-117