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arXiv · 2608.08052

Which numbers are $u$-invariants of perfectoid fields?

Eknath Ghate·Srinivasan Srimathy
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Abstract

Let $p\neq 2$ be a prime. We determine the set of numbers that occur as the $u$-invariant of perfectoid subfields of $\mathbb{C}_p$. Given any number that is the $u$-invariant of a field of characteristic $p$, we give an explicit construction of a perfectoid field with the same $u$-invariant. In particular, if a number is the $u$-invariant of a field of characteristic $p$, it is also the $u$-invariant of a field of characteristic zero.

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Eknath Ghate, Srinivasan Srimathy. 2026-08-08. Which numbers are $u$-invariants of perfectoid fields?. https://arxiv.org/abs/2608.08052

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