46 citations · 173 across the 30 of their papers we have counts for
13 papers · 1 filter
Remarks on the nonvanishing of cohomology groups for perverse sheaves on abelian varieties
Rainer Weissauer
It is shown that for a perverse sheaf on an abelian variety the integers for which the cohomology does not vanish define an interval in the number line (unde…
Vanishing theorems for abelian varieties over finite fields
Rainer Weissauer
For perverse sheaves K on abelian varieties X defined over a finitely generated field F we prove that the Euler-Poincare characteristic (defined for the extension of K to the algeb…
On the Tannaka group attached to the Theta divisor of a generic principally polarized abelian variety
Thomas Krämer, Rainer Weissauer
To any closed subvariety of a complex abelian variety one can attach a reductive algebraic group which is determined by the decomposition of the convolution powers of v…
Why certain Tannaka groups attached to abelian varieties are almost connected
Rainer Weissauer
We show that for a complex abelian variety X a certain Tannaka group G(X) attached to X is a pro-reductive group whose group of connected components is abelian, and hence isomorphi…
Degenerate Perverse Sheaves on Abelian Varieties
Rainer Weissauer
We analyze irreducible perverse sheaves on abelian varieties, defined over the complex numbers or the algebraic closure of a finite field, whose Euler characteristic is zero. We gi…
On the Rigidity of BN-sheaves
Rainer Weissauer
We define monoidal components attached to perverse sheaves on abelian varieties and discuss their properties.
A Remark on Rigidity of BN-sheaves
R. Weissauer
We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.
Vanishing Theorems for constructible Sheaves on Abelian Varieties
Thomas Krämer, Rainer Weissauer
We show that the hypercohomology of most character twists of perverse sheaves on a complex abelian variety vanishes in all non-zero degrees. As a consequence we obtain a vanishing…
On Subvarieties of Abelian Varieties with degenerate Gauss mapping
Rainer Weissauer
We show that for an irreducible subvariety Y of an abelian variety X the Gauss mapping, from the conormal bundle of to the dual of the tangent space of at the origin, is no…
Tannakian Categories attached to abelian Varieties
Rainer Weissauer
Starting from certain perverse sheaves on an abelian variety, including the intersection cohomology sheaves of curves and smooth ample divisors, we construct a semisimple super-Tan…
Torelli's theorem from the topological point of view
Rainer Weissauer
Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.
Brill-Noether Sheaves
Rainer Weissauer
We construct a -linear Tannakian category attached to a smooth projective curve C equivalent to the category of finite dimensional -representations Rep(G), wher…
A Siegel cusp form of degree 12 and weight 12
Richard E. Borcherds, E. Freitag, R. Weissauer
The theta series of the two unimodular even positive definite lattices of rank 16 are known to be linearly dependent in degree at most 3 and linearly independent in degree 4. In th…