A theorem of Matsushima
- 1 July 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 54, 123-134
- https://doi.org/10.1017/s0027763000024624
Abstract
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)).Keywords
This publication has 3 references indexed in Scilit:
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- Vector Bundles Over an Elliptic CurveProceedings of the London Mathematical Society, 1957
- On the Krull-Schmidt theorem with application to sheavesBulletin de la Société Mathématiques de France, 1956