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

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-Vaquié chain approximating $v_L$. This leads to explicit formulas for associated invariants such as the (absolute) (log) different, weight norm and Kähler 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.

53 pages, 0 figures, comments welcome