Non-existence of certain semistable abelian varieties
نویسندگان
چکیده
منابع مشابه
Semistable Abelian Varieties over Q
We prove that for N = 6 and N = 10, there do not exist any non-zero semistable abelian varieties over Q with good reduction outside primes dividingN . Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer–Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over Q with go...
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The semistable reduction theorem for curves was discussed in Christian’s notes. In these notes, we will use that result to prove an analogous theorem for abelian varieties. After some preliminaries on semi-abelian varieties (to convince us that the notion is a robust one), we will review the notion of a semi-abelian scheme (introduced in Christian’s lecture), recall the statement of the semista...
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Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work of researchers of the University of Warwick available open access under the following conditions. This article is made available under the Creative Commons Attribution 4.0 International license (CC BY 4.0) and may be reused according to the conditions of the license. For more details see: A note on versions: The ver...
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In an earlier work, we showed that if the Hodge conjecture holds for all complex abelian varieties of CM-type, then the Tate conjecture holds for all abelian varieties over finite fields (Milne 1999b). In this article, we extract from the proof a statement (Theorem 1.1) that sometimes allows one to deduce the Tate conjecture for the powers of a single abelian variety A over a finite field from ...
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2001
ISSN: 0025-2611
DOI: 10.1007/pl00005885