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On Morphisms Between Connected Commutative Algebraic Groups over a Field of Characteristic 0
Date de parution
2024
In
Transformation Groups
Vol.
29
No
4
De la page
1389
A la page
1403
Résumé
Let K be a field of characteristic 0 and let G and H be connected commutative algebraic groups over K. Let Mor_0(G,H) denote the set of morphisms of algebraic varieties G → H that map the neutral element to the neutral element. We construct a natural retraction from Mor_0(G,H) to Hom(G,H) (for arbitrary G and H) which commutes with the composition and addition of morphisms. In particular, if G and H are isomorphic as algebraic varieties, then they are isomorphic as algebraic groups. If G has no non-trivial unipotent group as a direct factor, we give an explicit description of the sets of all morphisms and isomorphisms of algebraic varieties between G and H. We also characterize all connected commutative algebraic groups over K whose only variety automorphisms are compositions of automorphisms of algebraic groups with translations.
Identifiants
Type de publication
journal article
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