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# Documents  14G17 | enregistrements trouvés : 5

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## Multi angle  The characteristic cycle and the singular support of an étale sheaf Saito, Takeshi (Auteur de la Conférence) | CIRM (Editeur )

We define the characteristic cycle of an étale sheaf on a smooth variety of arbitrary dimension in positive characteristic using the singular support, constructed by Beilinson very recently. The characteristic cycle satisfies a Milnor formula for vanishing cycles and an index formula for the Euler-Poincaré characteristic.

## Multi angle  Crystalline cohomology, period maps, and applications to K3 surfaces Liedtke, Christian (Auteur de la Conférence) | CIRM (Editeur )

I will first introduce K3 surfaces and determine their algebraic deRham cohomology. Next, we will see that crystalline cohomology (no prior knowledge assumed) is the "right" replacement for singular cohomology in positive characteristic. Then, we will look at one particular class of K3 surfaces more closely, namely, supersingular K3 surfaces. These have Picard rank 22 (note: in characteristic zero, at most rank 20 is possible) and form 9-dimensional moduli spaces. For supersingular K3 surfaces, we will see that there exists a period map and a Torelli theorem in terms of crystalline cohomology. As an application of the crystalline Torelli theorem, we will show that a K3 surface is supersingular if and only if it is unirational. I will first introduce K3 surfaces and determine their algebraic deRham cohomology. Next, we will see that crystalline cohomology (no prior knowledge assumed) is the "right" replacement for singular cohomology in positive characteristic. Then, we will look at one particular class of K3 surfaces more closely, namely, supersingular K3 surfaces. These have Picard rank 22 (note: in characteristic zero, at most rank 20 is possible) and form ...

## Multi angle  Fourier-Mukai partners of canonical covers in positive characteristic Tirabassi, Sofia (Auteur de la Conférence) | CIRM (Editeur )

We show that surfaces arising as canonical covers of Enriques and bielliptic surfaces do not have any non-trivial Fourier­Mukai partner, extending result of Sosna for complex surfaces. This is a joint work with K. Honigs and L. Lombardi.

## Multi angle  Differential descent obstructions Voloch, José Felipe (Auteur de la Conférence) | CIRM (Editeur )

We will discuss a new obstruction to the existence of rational and integral points on algebraic varieties over function fields obtained by considering covers described by differential equations.

## Multi angle  $D$-modules and $p$-curvatures Esnault, Hélène (Auteur de la Conférence) | CIRM (Editeur )

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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