Lecture notes introducing condensed mathematics as a framework for topology in algebraic and analytic settings.
Pseudocoherent and perfect complexes and vector bundles on analytic adic spaces
6 Pith papers cite this work. Polarity classification is still indexing.
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The p-adic monodromy theorem holds for families of G_K-equivariant vector bundles over the Fargues-Fontaine curve parametrized by algebraic-affinoid Q_p-algebras, enabling classification of line bundles without freeness assumptions.
Lecture notes use condensed mathematics to reprove finiteness of coherent cohomology, Serre duality, GAGA, and Hirzebruch-Riemann-Roch for compact complex manifolds.
Proves equivalence between smoothness of a rigid analytic variety and smoothness of its nuclear sheaves category in a six-functor formalism, relates compact generation to algebraization, and gives an example of a non-atomically generated internally smooth category.
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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Lectures on Condensed Mathematics
Lecture notes introducing condensed mathematics as a framework for topology in algebraic and analytic settings.
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The $p$-adic monodromy theorem over algebraic-affinoid algebras
The p-adic monodromy theorem holds for families of G_K-equivariant vector bundles over the Fargues-Fontaine curve parametrized by algebraic-affinoid Q_p-algebras, enabling classification of line bundles without freeness assumptions.
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Condensed Mathematics and Complex Geometry
Lecture notes use condensed mathematics to reprove finiteness of coherent cohomology, Serre duality, GAGA, and Hirzebruch-Riemann-Roch for compact complex manifolds.
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Smooth categories in a 6 functor formalism and compact generation for nuclear categories in analytic geometry
Proves equivalence between smoothness of a rigid analytic variety and smoothness of its nuclear sheaves category in a six-functor formalism, relates compact generation to algebraization, and gives an example of a non-atomically generated internally smooth category.
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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.
- Solid locally analytic representations