Timeline for Isomorphic endomorphism algebras implies isogenous (for abelian varieties over finite fields)?
Current License: CC BY-SA 4.0
4 events
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May 25, 2021 at 13:58 | vote | accept | Watson | ||
May 24, 2021 at 17:51 | comment | added | Yuri Zarhin | You are welcome. Yes, you understand it correctly: it certainly contradicts. The source of a mistake in the other answer is an improper use of Tate's theorem. Indeed, this theorem describes the local $v$-adic (or $\mathfrak{P}$-)invariants of the division algebra of endomorphisms. While these invariants lie in $Q/Z$, the other answer tacitly (and erroneously) assumes that they are rational numbers. | |
May 24, 2021 at 16:15 | comment | added | Watson | Thank you very much for this extended answer! I am going to read it, but just a quick question: you are considering the geometric endomorphism algebras, right (and not just the endomorphisms defined over $\mathbb F_{p^2}$)? Oh, I just saw that you mention this at the very end of your post. Because then your construction contradicts the other answer, if I understand correctly... ! | |
May 24, 2021 at 15:37 | history | answered | Yuri Zarhin | CC BY-SA 4.0 |