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Abstract:

The role of internal variability in generating an apparent link between autumn Barents‐Kara sea (BKS) ice and the winter North Atlantic Oscillation (NAO) has been intensely debated. In particular, the robustness and causality of the link has been questioned by showing that BKS‐NAO correlations exhibit nonstationarity in both reanalysis and climate model simulations. We show that the lack of ice observations means nonstationarity cannot be confidently assessed using reanalysis prior to 1961. Model simulations are used to corroborate an argument that forced nonstationarity could result from ice edge changes due to global warming. Consequently, the observed change in BKS‐NAO correlations since 1960 might not be purely a result of internal variability and may also reflect that the ice edge has moved. The change could also reflect the availability of more accurate ice observations. We discuss potential implications for analysis based on coupled climate models, which exhibit large ice edge biases.

Abstract:

Let (Formula presented.) be a field with (Formula presented.), where (Formula presented.) denotes the maximal pro-2 quotient of the absolute Galois group of a field (Formula presented.). We prove that then (Formula presented.) admits a (non-trivial) valuation (Formula presented.) which is 2-henselian and has residue field (Formula presented.). Furthermore, (Formula presented.) is a minimal positive element in the value group (Formula presented.) and (Formula presented.). This forms the first positive result on a more general conjecture about recovering (Formula presented.) -adic valuations from pro- (Formula presented.) Galois groups which we formulate precisely. As an application, we show how this result can be used to easily obtain number-theoretic information, by giving an independent proof of a strong version of the birational section conjecture for smooth, complete curves (Formula presented.) over (Formula presented.), as well as an analogue for varieties.