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# Documents  Colmez, Pierre | enregistrements trouvés : 5

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## Post-edited  Local acyclicity in $p$-adic geometry Scholze, Peter (Auteur de la Conférence) | CIRM (Editeur )

Motivated by applications to the geometric Satake equivalence and in particular the construction of the fusion product, we define a notion of universally locally acyclic for rigid spaces and diamonds, and prove that it has the expected properties.

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## Multi angle  Automorphy lifting via level lowering congruences Khare, Chandrashekhar (Auteur de la Conférence) | CIRM (Editeur )

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## Multi angle  A Jacobian criterion for smoothness of algebraic diamonds Fargues, Laurent (Auteur de la Conférence) | CIRM (Editeur )

(joint work with Peter Scholze) In our joint work with Scholze we need to give a meaning to statements like "the stack of principal G-bundles on the curve is smooth of dimension 0" and construct "smooth perfectoid charts on it". The problem is that in the perfectoid world there is no infinitesimals and thus no Jacobian criterion that would allow us to define what is a smooth morphism. The good notion in this setting is the one of a cohomologically smooth morphism, a morphism that satisfies relative Poincaré duality. I will explain a Jacobian criterion of cohomological smoothness for moduli spaces of sections of smooth algebraic varieties over the curve that allows us to solve our problems.
(joint work with Peter Scholze) In our joint work with Scholze we need to give a meaning to statements like "the stack of principal G-bundles on the curve is smooth of dimension 0" and construct "smooth perfectoid charts on it". The problem is that in the perfectoid world there is no infinitesimals and thus no Jacobian criterion that would allow us to define what is a smooth morphism. The good notion in this setting is the one of a coho...

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## Multi angle  On comparison theorems for rigid analytic spaces Niziol, Wieslawa (Auteur de la Conférence) | CIRM (Editeur )

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