Pierre Schapira - Sheaves for spacetimes @IhesFr

Uploaded June 2026 | Updated September 2026, 2 weeks ago

A causal manifold $(M,\lambda)$ is a real manifold $M$ endowed with a closed convex proper cone $\lambda$ in its cotangent bundle $T^*M$.
On such a manifold, one defines the $\lambda$-topology and the past or the future of any subset.
A time function is a smooth surjective causal map $q: M\to\mathbb R$ proper on the past or future of any compact subset of $M$.
Using a time function, we show that if the micro-support of a sheaf $F$ does not intersect $\lambda\cup-\lambda$ outside of the zero-section, then for any Cauchy hypersurface $N_t=q^{-1}(t)$, the restriction morphism
$\mathrm{R}\Gamma(M;F)\to\mathrm{R}\Gamma(N_t;F\vert_{N_t})$ is an isomorphism. As an application, we get that the Cauchy problem is globally well-posed for hyperfunction solutions of hyperbolic systems.

Pierre Schapira (Institut de mathématiques Jussieu-Paris Rive Gauche)

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Find this and many more scientific videos on carmin.tv - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.

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$Pierre Schapira - Sheaves for spacetimes A causal manifold $(M,lambda)$ is a real manifold $M$ endowed with a closed convex proper cone $lambda$ in its cotangent bundle $T^*M$. On such a manifold, one defines the $lambda$-topology and the past or the future of any subset. A time function is a smooth surjective causal map $q: Mtomathbb R$ proper on the past or future of any compact subset of $M$. Using a time function, we show that if the micro-support of a sheaf $F$ does not intersect $lambdacup-lambda$ outside of the zero-section, then for any Cauchy hypersurface $N_t=q^{-1}(t)$, the restriction morphism $mathrm{R}Gamma(M;F)tomathrm{R}Gamma(N_t;Fvert_{N_t})$ is an isomorphism. As an application, we get that the Cauchy problem is globally well-posed for hyperfunction solutions of hyperbolic systems. Pierre Schapira (Institut de mathématiques Jussieu-Paris Rive Gauche) Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.$

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