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Travaux de Zink

William Messing (2005/2006)

Séminaire Bourbaki

The diverse Dieudonné theories have as their common goal the classification of formal groups and p -divisible groups. The most recent theory is Zink’s theory of displays. A display over a ring R is a finitely generated projective module over the ring of Witt vectors, W ( R ) , equipped with additional structures. Zink has shown that using this notion, more concrete than those previously defined, one can obtain a good theory and prove an equivalence theorem in great generality. I will give an overview of...

Triangularization properties of power linear maps and the Structural Conjecture

Michiel de Bondt, Dan Yan (2014)

Annales Polonici Mathematici

We discuss several additional properties a power linear Keller map may have. The Structural Conjecture of Drużkowski (1983) asserts that certain two such properties are equivalent, but we show that one of them is stronger than the other. We even show that the property of linear triangularizability is strictly in between. Furthermore, we give some positive results for small dimensions and small Jacobian ranks.

Triangulation in o-minimal fields with standard part map

Lou van den Dries, Jana Maříková (2010)

Fundamenta Mathematicae

In answering questions of J. Maříková [Fund. Math. 209 (2010)] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V, and let st: V → k be the corresponding standard part map. Under a mild assumption on (R,V) we show that a definable set X ⊆ Vⁿ admits a triangulation that induces a triangulation of its standard part st X ⊆ kⁿ.

Trivial points on towers of curves

Xavier Xarles (2013)

Journal de Théorie des Nombres de Bordeaux

In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.

Troesch complexes and extensions of strict polynomial functors

Antoine Touzé (2012)

Annales scientifiques de l'École Normale Supérieure

We develop a new approach of extension calculus in the category of strict polynomial functors, based on Troesch complexes. We obtain new short elementary proofs of numerous classical Ext -computations as well as new results. In particular, we get a cohomological version of the “fundamental theorems” from classical invariant theory for  G L n for  n big enough (and we give a conjecture for smaller values of  n ). We also study the “twisting spectral sequence” E s , t ( F , G , r ) converging to the extension groups Ext 𝒫 𝕜 * ( F ( r ) , G ( r ) ) between the...

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