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Fixed-point free automorphisms of abelian varieties

Identifieur interne : 001E21 ( Main/Merge ); précédent : 001E20; suivant : 001E22

Fixed-point free automorphisms of abelian varieties

Auteurs : Ch. Birkenhake [Allemagne] ; H. Lange [Allemagne]

Source :

Geometriae Dedicata [ 0046-5755 ] ; 1994-07-01.

RBID : ISTEX:3220709C87FD19D382D43D16FC833A718468217C

English descriptors

KwdEn :
- Abelian, Abelian surfaces, Abelian varieties, Abelian variety, Analytic representation, Automorphism, Automorphisms, Canonical, Canonical isomorphism, Commutative, Complex multiplication, Elliptic, Elliptic curve, Elliptic curves, Endomorphism, Free automorphism, Free automorphisms, Higher dimensions, Isomorphism, Lefschetz, Lefschetz formula, Number field, Other hand, Period matrix, Principal order, Real multiplication, Simple abelian surface, Simple abelian surfaces, Simple abelian varieties, Simple abelian variety.
Teeft :
- Abelian, Abelian surfaces, Abelian varieties, Abelian variety, Analytic representation, Automorphism, Automorphisms, Canonical, Canonical isomorphism, Commutative, Complex multiplication, Elliptic, Elliptic curve, Elliptic curves, Endomorphism, Free automorphism, Free automorphisms, Higher dimensions, Isomorphism, Lefschetz, Lefschetz formula, Number field, Other hand, Period matrix, Principal order, Real multiplication, Simple abelian surface, Simple abelian surfaces, Simple abelian varieties, Simple abelian variety.

Abstract

Abstract: An automorphismf of an abelian varietyX is called fixed point free if it admits no fixed points other than the origin and this is of multiplicity one. It is well known that the elliptic curve withj-invariant 0 is the only elliptic curve admitting a fixed point free automorphism. In this note, this result is extended to abelian varieties of higher dimensions and some connected commutative algebraic groups.

Url:

https://api.istex.fr/document/3220709C87FD19D382D43D16FC833A718468217C/fulltext/pdf

DOI: 10.1007/BF01263993

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Le document en format XML

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<term>Isomorphism</term>
<term>Lefschetz</term>
<term>Lefschetz formula</term>
<term>Number field</term>
<term>Other hand</term>
<term>Period matrix</term>
<term>Principal order</term>
<term>Real multiplication</term>
<term>Simple abelian surface</term>
<term>Simple abelian surfaces</term>
<term>Simple abelian varieties</term>
<term>Simple abelian variety</term>
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<term>Abelian surfaces</term>
<term>Abelian varieties</term>
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<term>Automorphisms</term>
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<term>Canonical isomorphism</term>
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<term>Lefschetz</term>
<term>Lefschetz formula</term>
<term>Number field</term>
<term>Other hand</term>
<term>Period matrix</term>
<term>Principal order</term>
<term>Real multiplication</term>
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<front><div type="abstract" xml:lang="en">Abstract: An automorphismf of an abelian varietyX is called fixed point free if it admits no fixed points other than the origin and this is of multiplicity one. It is well known that the elliptic curve withj-invariant 0 is the only elliptic curve admitting a fixed point free automorphism. In this note, this result is extended to abelian varieties of higher dimensions and some connected commutative algebraic groups.</div>
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Fixed-point free automorphisms of abelian varieties

Fixed-point free automorphisms of abelian varieties

Source :

English descriptors

Abstract

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