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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
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Fibration exact sequence in homotopy vs spectral sequence in (co)homology
Perhaps this should be obvious but why is it that one may associate to a fibration exact sequences of topological spaces a long exact sequence of fundamental groups, but in (co)homology, one only has …
5
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Relative algebraic $K$ theory of Galois extensions
Let $R$ be a domain, e.g. $\mathbb{Z}$, and let $R\to R[x]/I$ be an integral extension, e.g $\mathbb{Z}[i]$.
Is anything known about the relative algebraic $K$ groups, $K_*(R',R)$? For example, when $ …
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Topological Hochschild Homology and $p$-adic étale cohomology of $\mathbb{Q}$-schemes
Recent progress in $p$-adic geometry has produced an interesting comparison isomorphism between the crystalline cohomology of a smooth algebra $A$ over a perfect field $k$ in characteristic $p$, and t …