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Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.

Hodge Spectral Sequence on Pseudoconvex Domains.

Takeo Ohsawa, Kensho Takegoshi (1988)

Mathematische Zeitschrift

Hodge type of subvarieties of compact hermitian symmetric spaces.

Pedro L. Del Angel (1996)

Mathematische Zeitschrift

Hodge type of subvarieties of IPn of small degrees.

Hélène Esnault (1990)

Mathematische Annalen

Hodge-Tate and de Rham representations in the imperfect residue field case

Kazuma Morita (2010)

Annales scientifiques de l'École Normale Supérieure

Let $K$ be a $p$ -adic local field with residue field $k$ such that $[k : k^{p}] = p^{e} < + \infty$ and $V$ be a $p$ -adic representation of $Gal (\bar{K} / K)$ . Then, by using the theory of $p$ -adic differential modules, we show that $V$ is a Hodge-Tate (resp. de Rham) representation of $Gal (\bar{K} / K)$ if and only if $V$ is a Hodge-Tate (resp. de Rham) representation of $Gal (\bar{K^{pf}} / K^{pf})$ where $K^{pf} / K$ is a certain $p$ -adic local field with residue field the smallest perfect field $k^{pf}$ containing $k$ .

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Harmonic gauges on Riemann surfaces and stable bundles

Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties.

H*(C/B,L) for G of semi-simple rank 2

Hecke curves and Hitchin discriminant

Helices on some Fano threefolds : constructivity of semiorthogonal bases of $K_{0}$

Higher de Rham-Witt complexes of supersingular K3 surfaces

Higher direct images of canonical sheaves tensorized with semi-positive vector bundles by proper Kähler morphisms.

Higher order operations in Deligne cohomology.

Higher solutions of hypergeometric systems and Dwork cohomology

Hilbert-Samuel Polynomials of a Proper Morphism.

Hochschild cohomology of complex spaces and Noetherian schemes.

Hodge filtrations and the higher direct images of canonical sheaves.

Hodge metrics and the curvature of higher direct images

Hodge Spectral Sequence on Pseudoconvex Domains.

Hodge type of subvarieties of compact hermitian symmetric spaces.

Hodge type of subvarieties of IPn of small degrees.

Hodge-Tate and de Rham representations in the imperfect residue field case

Hodge-Tate periods and p-adic abelian integrals.

Höhere Sekantenvarietäten und Vektorbündel auf Kurven.

Holomorphe Differentialformen auf algebraischen Varietäten mit Singularitäten I.

Currently displaying 1 – 20 of 41