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arXiv · 1710.03404

Deformations of overconvergent isocrystals on the projective line

Shishir Agrawal
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Abstract

Let $k$ be a perfect field of positive characteristic and $Z$ an effective Cartier divisor in the projective line over $k$ with complement $U$. In this note, we establish some results about the formal deformation theory of overconvergent isocrystals on $U$ with fixed "local monodromy" along $Z$. En route, we show that a Hochschild cochain complex governs deformations of a module over an arbitrary associative algebra. We also relate this Hochschild cochain complex to a de Rham complex in order to understand the deformation theory of a differential module over a differential ring.

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Shishir Agrawal. 2019-06-26. Deformations of overconvergent isocrystals on the projective line. https://doi.org/10.1016/j.jnt.2019.11.013

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