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arXiv · 1501.05294

A Deligne pairing for Hermitian Azumaya modules

Fabian Reede
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Abstract

In this short note we want to give a definition of a generalized Deligne pairing for modules over an Azumaya algebra on an arithmetic surface $X$. We do this by defining Hermitian metrics on the Azumaya algebra and on the modules in question. Then we go on and define the determinant of the cohomology for a pair of modules over an Azumaya algebra. Using this we give the definition of a generalized Deligne pairing and study some of its properties.

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Fabian Reede. 2015-01-21. A Deligne pairing for Hermitian Azumaya modules. https://arxiv.org/abs/1501.05294

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