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arXiv · 2604.01992

The integral (log) cotangent complex of extensions of valued fields

Michaël Maex
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Abstract

Let $(L, v_L) / (K, v_K)$ be a finite or purely transcendental extension of real valued fields. We construct the associated integral cotangent and log cotangent complexes in terms of a MacLane-Vaqui\'e chain approximating $v_L$. This leads to explicit formulas for associated invariants such as the (absolute) (log) different, weight norm and K\"ahler norm. As a corollary of our methods we obtain strong control of the higher homology of the integral (log) cotangent complex, generalizing an important result of Gabber and Ramero to the logarithmic setting.

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Michaël Maex. 2026-04-02. The integral (log) cotangent complex of extensions of valued fields. https://arxiv.org/abs/2604.01992

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