有限或纯超越值域扩张的积分（对数）余切复物
The integral (log) cotangent complex of extensions of valued fields
AI总结：
本文构造了实值域扩张的积分和对数余切复物，通过MacLane-Vaquié链近似估值，得到相关不变量的显式公式，并推广Gabber和Ramero的结果至对数情形。
摘要：
设(L, v_L)/(K, v_K)为有限或纯超越实值域扩张。我们构造了相关的积分余切和对数余切复物，基于MacLane-Vaquié链近似v_L。这导致了诸如绝对（对数）微分、重量范数和Kähler范数等关联不变量的显式公式。作为我们方法的推论，我们获得了积分（对数）余切复物的高阶同调的强控制，将Gabber和Ramero的重要结果推广到对数情形。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
