Displaying similar documents to “Étale cohomology and reduction of abelian varieties”

Simplicity of twists of abelian varieties

Alex Bartel (2015)

Acta Arithmetica

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We give some easy necessary and sufficient criteria for twists of abelian varieties by Artin representations to be simple.

Intersection cohomology of reductive varieties

Roy Joshua, Michel Brion (2004)

Journal of the European Mathematical Society

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We extend the methods developed in our earlier work to algorithmically compute the intersection cohomology Betti numbers of reductive varieties. These form a class of highly symmetric varieties that includes equivariant compactifications of reductive groups. Thereby, we extend a well-known algorithm for toric varieties.

Describing toric varieties and their equivariant cohomology

Matthias Franz (2010)

Colloquium Mathematicae

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Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated...

Weights in the cohomology of toric varieties

Andrzej Weber (2004)

Open Mathematics

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We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complexIH T*(X)⊗H*(T). We also describe the weight filtration inIH *(X).

Realization of long exact sequences of abelian groups.

Irwin S. Pressman (1990)

Publicacions Matemàtiques

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Given a long exact sequence of abelian groups L: ... → Li-1 →ξi-1 Li →ξi Li+1 → ... a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized. Two techniques which are introduced...