Proves Virtual Surjection Conjecture and n-(n+1)-(n+2) Conjecture for profinite groups via a numerical criterion for FP_n of modules.
Relative p-adic hodge theory, II: Imperfect period rings
7 Pith papers cite this work, alongside 53 external citations. Polarity classification is still indexing.
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UNVERDICTED 7representative citing papers
The category of pro-étale vector bundles on a proper rigid-analytic variety X over C is equivalent to the category of Higgs bundles on the eh-site of X.
Proves semistable reduction for E^dag_K-valued and K-valued overconvergent F-isocrystals on k((t))-varieties, implying finite-dimensionality of compactly supported rigid cohomology.
Proves relative p-adic monodromy theorem over dense open set and equivalence to Newton polygon constancy near rank-1 points for de Rham local systems, plus extension of conjecture to Newton partition interiors.
On perfectoid spaces over p-adic fields, étale and v-topological G-torsors coincide for arbitrary rigid analytic groups G, generalizing prior results for Ga and GL_n, with applications to generalized Q_p-representations equaling v-vector bundles.
Lecture notes present liquid real vector spaces and a tentative category of analytic spaces as part of work toward analytic stacks, though the definition was later abandoned.
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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Virtual Surjection and the $n$-$(n+1)$-$(n+2)$ Theorem for Profinite Groups
Proves Virtual Surjection Conjecture and n-(n+1)-(n+2) Conjecture for profinite groups via a numerical criterion for FP_n of modules.
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A $p$-adic Simpson correspondence for singular rigid-analytic varieties
The category of pro-étale vector bundles on a proper rigid-analytic variety X over C is equivalent to the category of Higgs bundles on the eh-site of X.
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Semistable Reduction Theorem for Overconvergent $F$-isocrystals over Laurent Series Fields
Proves semistable reduction for E^dag_K-valued and K-valued overconvergent F-isocrystals on k((t))-varieties, implying finite-dimensionality of compactly supported rigid cohomology.
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p-adic Hodge theory of de Rham local systems, I: Newton polygon and monodromy
Proves relative p-adic monodromy theorem over dense open set and equivalence to Newton polygon constancy near rank-1 points for de Rham local systems, plus extension of conjecture to Newton partition interiors.
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$G$-torsors on perfectoid spaces
On perfectoid spaces over p-adic fields, étale and v-topological G-torsors coincide for arbitrary rigid analytic groups G, generalizing prior results for Ga and GL_n, with applications to generalized Q_p-representations equaling v-vector bundles.
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Lectures on Analytic Geometry
Lecture notes present liquid real vector spaces and a tentative category of analytic spaces as part of work toward analytic stacks, though the definition was later abandoned.
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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.