Geodesic
Fiber integration of gerbes and Deligne line bundles
Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 21-51.

Voir la notice de l'article provenant de la source International Press of Boston

Let $\pi : X \to S$ be a family of smooth projective curves, and let $L$ and $M$ be a pair of line bundles on $X$. We show that Deligne’s line bundle $\langle L,M \rangle$ can be obtained from the $\mathcal{K}_2$-gerbe $G_{L,M}$ constructed in [AR16] via an integration along the fiber map for gerbes that categorifies the well known one arising from the Leray spectral sequence of $\pi$. Our construction provides a full account of the biadditivity properties of $\langle L,M \rangle$. Our main application is to the categorification of correspondences on the self-product of a curve. The functorial description of the low degree maps in the Leray spectral sequence for $\pi$ that we develop is of independent interest, and, along the way, we provide an example of their application to the Brauer group.
DOI : 10.4310/HHA.2023.v25.n1.a2
Classification : 14C25, 14F42, 55N15, 55P20
Keywords: algebraic cycle, gerbe, higher category 
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     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n1.a2/}
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Ettore Aldrovandi; Niranjan Ramachandran. Fiber integration of gerbes and Deligne line bundles. Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 21-51. doi : 10.4310/HHA.2023.v25.n1.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n1.a2/

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