P-adic lattices are not K\"ahler groups

In this note we show that any lattice in a simple p-adic Lie group is not the fundamental group of a compact Ka\"hler manifold, as well as some variants of this result.Comment: Final versio

Oxidation resistant, thoria-dispersed nickel-chromium-aluminum alloy

Modified thoria-dispersed nickel-chromium alloy has been developed that exhibits greatly improved resistance to high-temperature oxidation. Additions of aluminum have been made to change nature of protective oxide scale entirely and to essentially inhibit oxidation at temperatures up to 1260 C

Symmetric differentials and the fundamental group

Esnault asked whether every smooth complex projective variety with infinite fundamental group has a nonzero symmetric differential (a section of a symmetric power of the cotangent bundle). In a sense, this would mean that every variety with infinite fundamental group has some nonpositive curvature. We show that the answer to Esnault's question is positive when the fundamental group has a finite-dimensional representation over some field with infinite image. This applies to all known varieties with infinite fundamental group. Along the way, we produce many symmetric differentials on the base of a variation of Hodge structures. One interest of these results is that symmetric differentials give information in the direction of Kobayashi hyperbolicity. For example, they limit how many rational curves the variety can contain.Comment: 14 pages; v3: references added. To appear in Duke Math.

On the second cohomology of K\"ahler groups

Carlson and Toledo conjectured that any infinite fundamental group $\Gamma$ of a compact K\"ahler manifold satisfies $H^2(\Gamma,\R)\not =0$. We assume that $\Gamma$ admits an unbounded reductive rigid linear representation. This representation necessarily comes from a complex variation of Hodge structure (\C-VHS) on the K\"ahler manifold. We prove the conjecture under some assumption on the \C-VHS. We also study some related geometric/topological properties of period domains associated to such \C-VHS.Comment: 21 pages. Exposition improved. Final versio