We give explicit harmonic representatives of Dolbeault cohomology Oeljeklaus-Toma manifolds and show that they are geometrically formal. also Bott-Chern type $(s,1)$ study the Angella-Tomassini inequality.

We suggest a new combinatorial construction for the cohomology ring of the ag manifold. The degree 2 commutation relations satissed by the divided diierence operators corresponding to positive roots deene a quadratic associative algebra. In this algebra, the formal analogues of Dunkl operators generate a commuta-tive subring, which is shown to be canonically isomorphic to the cohomology of the ...

Displays were introduced to classify formal p-divisible groups over an arbitrary ring R where p is nilpotent. We define a more general notion of display and obtain an exact tensor category. In many examples the crystalline cohomology of a smooth and proper scheme X over R carries a natural display structure. It is constructed from the relative de Rham-Witt complex. For this we refine the compar...

Let R be a polynomial ring in finitely many variables over the integers, and fix an ideal a of R. We prove that for all but finitely prime integers p, the Bockstein homomorphisms on local cohomology, H a (R/pR) −→ H k+1 a (R/pR), are zero. This provides strong evidence for Lyubeznik’s conjecture which states that the modules H a (R) have a finite number of associated prime ideals.

Let Y be a divisor on a smooth algebraic variety X. We investigate the geometry of the Jacobian scheme of Y , homological invariants derived from logarithmic differential forms along Y , and their relationship with the property that Y be a free divisor. We consider arrangements of hyperplanes as a source of examples and counterexamples. In particular, we make a complete calculation of the local...

Let V be a holomorphic vector bundle on a complex manifold M , with a flat connection ∇. We shall make the following three assumptions: (1) M is an open subset of a bigger complex manifold M . (2) The boundary D = M \M is a divisor with normal crossing singularities. (3) The connection ∇ is unipotent along D. Under these assumptions, V has a canonical extension to a vector bundle V on M . Since...

We study the relationship between the Frobenius stability of an Artinian module over an F-injective ring and its stable part.