On the mixed Hodge structure associated to <span class="mathjax-formula">$\pi _3$</span> of a simply connected complex projective manifold

• freeness of the integral cohomology of a Hilbert modular variety over certain local components of the Hecke algebra and Gorenstein property of these local algebras.. We study

It seems that the first result in the literature which is related to Borel's conjecture is a result of Harder for the rank 1 case, which states that every de Rham cohomology class has

- Let K be a perfect field of characteristic p&gt;0, and X/W(K) aprojective smooth W-scheme with geometrically connected fibres whose Hodge cohomology groups are

In our case, a connected component E» of E must lie in a fiber F; of/. The isomorphism [Fo]^ preserves the cohomology class of the fibering peH^Xo.Z), and hence, by lemma 5.5 and

arithmetic Kleinian group. Borel’s maximal groups can be described as certain of these images of normalizers of Eichler orders. - Small arithmetic orbifolds with little

In this paper, we observe that so much is known about the structure of 3- manifolds and that the Baum-Connes Conjecture With Coefficients has been proved for such a large class of

solve completely; the resulting solutions give rise to Weierstrass models of elliptic curves EIK with good reduction everywhere, with the possible exception of the

(We should mention that Hodge theory and function theory on singular manifolds has been considered by a number of authors. A cohomology theory on Euclidean buildings was developed by