Ogus's conjecture is resolved affirmatively in full generality by constructing the required F-isocrystal via p-adic local systems and prismatic methods, while also introducing a prismatic refinement of the p-adic Riemann-Hilbert functor.
On the rationalization of the $K(n)$-local sphere
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We compute the rational homotopy groups of the $K(n)$-local sphere for all heights $n$ and all primes $p$, verifying a prediction that goes back to the pioneering work of Morava in the early 1970s. More precisely, we show that the inclusion of the Witt vectors into the Lubin-Tate ring induces a split injection on continuous stabilizer cohomology with torsion cokernel of bounded exponent, thereby proving Hopkins' chromatic splitting conjecture and the vanishing conjecture of Beaudry-Goerss-Henn rationally. The key ingredients are the equivalence between the Lubin-Tate tower and the Drinfeld tower due to Faltings and Scholze-Weinstein, integral $p$-adic Hodge theory, and an integral refinement of a theorem of Tate on the Galois cohomology of non-archimedean fields.
years
2026 4representative citing papers
New transparent proof of Drinfeld's representability theorem for moduli of p-divisible groups with extra actions, plus detailed presentation of the moduli space and formal model of the p-adic symmetric space.
Explores locality of mod p GL_2 representations over unramified quadratic extensions of Q_p by constructing a candidate representation of a subgroup via perfectoid geometry.
citing papers explorer
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Ogus's conjecture on F-isocrystals
Ogus's conjecture is resolved affirmatively in full generality by constructing the required F-isocrystal via p-adic local systems and prismatic methods, while also introducing a prismatic refinement of the p-adic Riemann-Hilbert functor.
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On Drinfeld's representability theorem
New transparent proof of Drinfeld's representability theorem for moduli of p-divisible groups with extra actions, plus detailed presentation of the moduli space and formal model of the p-adic symmetric space.
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To be or not to be local
Explores locality of mod p GL_2 representations over unramified quadratic extensions of Q_p by constructing a candidate representation of a subgroup via perfectoid geometry.
- Higher Semiadditive Character Theory