5 мая 2015 г. · Let k be a field and X an algebraic variety over k. I have often seen people write Aut(X/k) for the automorphisms "defined over k".

20 мар. 2014 г. · The K-algebra structure on Spec(A) is uniquely given by a homomorphism K→A; that is, a scheme morphism Spec(A)→Spec(K). A ring homomorphism B→A ...

19 апр. 2020 г. · Morphism of k-schemes ... Let k be an algebraically closed field. Let X be a k-scheme. I have been asked to "describe" the k-scheme morphisms of ...

29 дек. 2014 г. · That map is given by sending a morphism f:Spec(K)→X to the value f((0)) of the only prime ideal in K. Why is this map injective? I don't ...

3 мая 2021 г. · If K is a field and X→SpecK a K-scheme, and I have two morphisms of K-schemes f1,f2:SpecK→X that are different, does it follow that f1 and f2 ...

7 янв. 2014 г. · Let f,g:X→Y be two morphisms of k-schemes such that the induced morphisms : X(¯k)→Y(¯k) are equal. How does one show that f=g. There is a hint ...

21 мая 2017 г. · The restriction to L1 of any K-morphism f:L→Ω is a K-homomorphism f1 from L1 to Ω. I'm asking myself what K-morphism means in this context. In ...

13 мар. 2020 г. · Since k[[t]] is a DVR with a uniformizer t, the kernel has to be of the form (tn) for some n, and so φ factors through k[[t]]/(tn)=k[t]/(tn).

24 мар. 2016 г. · A K-morphism can be an isomorphism, wich comes to being surjective as well. If in that case also L=M then you are dealing with a K-automorphism.

23 апр. 2021 г. · A morphism f:X⟶Y of k-varieties induces a map from the k-rational points of X to the k-rational points of Y.