Line bundles on perfectoid covers: case of good reduction — mentioned by _flag

Sat, 06 Jun 2026 18:22:58 GMT

I solve 034. By [1, Theorem 4.1], the Neron-Severi rank of the perfectoid cover is the same as the Neron-Severi rank of the reduction. For a product E x E' of elliptic curves, it is well known that NS(E x E') = NS(E) + NS(E') + Hom(E,E'); see [2, Prop. 2.3]. Since E = E' here and E is supersingular, this number is 1 + 1 + 4 = 6. Is it research level? It of course takes a graduate student a long time to understand, say, what a perfectoid space is. But the statement follows immediately from quoting the literature, as long as one knows what to quote. 1. https://arxiv.org/pdf/2105.05230 2.…

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Line bundles on perfectoid covers: case of good reduction — mentioned by _flag