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# Documents  Nicaise, Johannes | enregistrements trouvés : 10

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## The non-archimedean SYZ fibration and Igusa zeta functions - Part 1 Nicaise, Johannes | CIRM H

Post-edited

Research talks;Algebraic and Complex Geometry

The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint work with Mircea Mustata and Chenyang Xu. The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint ...

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## An overview on some recent results about $p$-adic differential equations over Berkovich curves Pulita, Andrea | CIRM H

Post-edited

Research talks;Partial Differential Equations;Algebraic and Complex Geometry

I will give an introductory talk on my recent results about $p$-adic differential equations on Berkovich curves, most of them in collaboration with J. Poineau. This includes the continuity of the radii of convergence of the equation, the finiteness of their controlling graphs, the global decomposition by the radii, a bound on the size of the controlling graph, and finally the finite dimensionality of their de Rham cohomology groups, together with some local and global index theorems relating the de Rham index to the behavior of the radii of the curve. If time permits I will say a word about some recent applications to the Riemann-Hurwitz formula. I will give an introductory talk on my recent results about $p$-adic differential equations on Berkovich curves, most of them in collaboration with J. Poineau. This includes the continuity of the radii of convergence of the equation, the finiteness of their controlling graphs, the global decomposition by the radii, a bound on the size of the controlling graph, and finally the finite dimensionality of their de Rham cohomology groups, together ...

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## The non-archimedean SYZ fibration and Igusa zeta functions - Part 2 Nicaise, Johannes | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint work with Mircea Mustata and Chenyang Xu. The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint ...

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## The non-archimedean SYZ fibration and Igusa zeta functions - Part 3 Nicaise, Johannes | CIRM H

Multi angle

Research talks
;Algebraic and Complex Geometry

The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint work with Mircea Mustata and Chenyang Xu. The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint ...

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## de Rham theorem in non-Archimedean analytic geometry Berkovich, Vladimir | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

In my work in progress on complex analytic vanishing cycles for formal schemes, I have defined integral "etale" cohomology groups of a compact strictly analytic space over the field of Laurent power series with complex coefficients. These are finitely generated abelian groups provided with a quasi-unipotent action of the fundamental group of the punctured complex plane, and they give rise to all $l$-adic etale cohomology groups of the space. After a short survey of this work, I will explain a theorem which, in the case when the space is rig-smooth, compares those groups and the de Rham cohomology groups of the space. The latter are provided with the Gauss-Manin connection and an additional structure which allow one to recover from them the "etale" cohomology groups with complex coefficients. In my work in progress on complex analytic vanishing cycles for formal schemes, I have defined integral "etale" cohomology groups of a compact strictly analytic space over the field of Laurent power series with complex coefficients. These are finitely generated abelian groups provided with a quasi-unipotent action of the fundamental group of the punctured complex plane, and they give rise to all $l$-adic etale cohomology groups of the space. ...

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## $D$-modules and $p$-curvatures Esnault, Hélène | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

We show relations between rigidity of connections in characteristic 0 and nilpotency of their $p$-curvatures (a consequence of a conjecture by Simpson and of a generalization of Grothendieck's $p$-curvature conjecture).
Work in progress with Michael Groechenig.

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## Arithmetic $D$-modules and existence of crystalline companion Abe, Tomoyuki | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

We will show that there exists a correspondence between smooth $l$-adic sheaves and overconvergent $F$-isocrystals over a curve preserving the Frobenius eigenvalues. Moreover, we show the existence of $l$-adic companions associated to overconvergent $F$-isocrystals for smooth varieties.
Some part of the work is done jointly with Esnault.

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## Explosion of Lyapunov exponents using non-Archimedean geometry Favre, Charles | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

We consider a meromorphic family of endomorphisms of the complex projective space parameterized by the unit disk, and show that the blow-up of the Lyapunov exponent near the origin is controlled by a non-Archimedean quantity.

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## Motivic integration and its interactions with model theory and non-Archimedean geometry.Volume II Cluckers, Raf ; Nicaise, Johannes ; Sebag, Julien | Cambridge University Press 2011

Ouvrage

- xii; 250 p.
ISBN 978-1-107-64881-4

London mathematical society lecture note series , 0384

Localisation : Collection 1er étage

géométrie algébrique # corps valués # théorie des modèles # espaces analytiques

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## Motivic integration Chambert-Loir, Antoine ; Nicaise, Johannes ; Sebag, Julien | Birkhäuser 2018

Ouvrage

- xx; 526 p.
ISBN 978-1-4939-7885-4

Progress in mathematics , 0325

Localisation : Collection 1er étage

géométrie algébrique # K-théorie # intégration motivique # anneau de Grothendieck # schéma de Greenberg # géométrie birationnelle # géométrie non Archimédienne

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