Documents  14G17 | enregistrements trouvés : 9

- vi; 348 p.
ISBN 978-3-03719-182-8

EMS series of congress reports

Localisation : Colloque 1er étage (BEDL)

Friedrich Hirzebruch # variété de Schubert # géométrie algébrique

14-06 ; 14L10 ; 14M15 ; 14J27 ; 32M10 ; 32M15 ; 00B25 ; 32L10 ; 55N91 ; 14C17 ; 14G17

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Research talks

In this talk, starting from the perspective of characteristic zero, I will discuss pathologies for the generic fibre of Fano fibrations in characteristic p.
The new approach of the joint project with Stefan Schröer has two goals:
- controlling these pathological phenomena; and
- describing new examples.
I'm going to focus on dimension 3, motivated by the recent progress in Mori theory in positive characteristic.

14J45 ; 14E30 ; 14G17

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Research talks;Algebraic and Complex Geometry;Number Theory

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.

14F20 ; 14G17 ; 11S15

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Research talks;Algebraic and Complex Geometry

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 ...

14J28 ; 14G17 ; 14M20 ; 14D22

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Research talks;Algebraic and Complex Geometry

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

14F05 ; 14J28 ; 14G17 ; 14K12

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Research talks;Algebraic and Complex Geometry;Number Theory

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.

11G35 ; 14G17

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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.

14D05 ; 14E20 ; 14F05 ; 14F35 ; 14G17

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- 125 p.
ISBN 978-2-85629-861-9

Astérisque , 0391

Localisation : Périodique 1er étage

motif mixte # topologie de Grothendieck # altération # filtration par tranche # groupe de Chow supérieur

14-XX ; 14F42 ; 32S45 ; 14C15 ; 14E15 ; 14G17 ; 19E15 ; 14C25 ; 14F20 ; 18E30 ; 13D15

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