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.
Introduces solid locally analytic representations of p-adic Lie groups with category equivalences to modules and sheaves, generalizing classical results and extending cohomological comparisons.
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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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.