Timeline for Notation for endomorphism algebra of Elliptic Curves

6 events

when toggle format	what		by	license	comment
Nov 3, 2018 at 5:21	comment	added	user19475		For motives there is the notion of correspondences of degree $r$. One has $\mathrm{Corr}^0(X,Y) = \mathrm{Hom}(h(X),h(Y))$. See e.g. Scholl's article in the Motives volume I. The Hom between $h^1$ is the group of isogenies, $\mathrm{End}_{\mathcal{M}_\mathbf{Q}}(h^1(E)) = \mathrm{End}(E) \otimes_\mathbf{Z} \mathbf{Q}$ (Proposition 4.5).
Nov 3, 2018 at 3:27	history	edited	Michael Hardy	CC BY-SA 4.0	added 48 characters in body
Nov 3, 2018 at 2:15	comment	added	Joe Silverman		Not sure if this is the earliest usage, but it's the notation that Mumford uses in his classic book on Abelian Varieties. Indeed, he defines $\text{Hom}^0(X,Y)=\mathbb{Q}\otimes_{\mathbb{Z}}\text{Hom}(X,Y)$, as well as the analogous notation for End. This gives a new category in which the objects are abelian varieties and the morphisms are in Hom$^0$, which Mumford says is "the so-called category of 'abelian varieties up to isogeny'."
Nov 2, 2018 at 22:50	review	First posts
Nov 3, 2018 at 1:35
Nov 2, 2018 at 22:49	comment	added	Wojowu		I doubt it means anything beyond "the thing tensored with $\mathbb Q$". To the best of my knowledge, there is no such thing as $End^1$.
Nov 2, 2018 at 22:46	history	asked	MachPortMassenger	CC BY-SA 4.0