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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.

51 votes
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Separable and algebraic closures?

Geometrically there is a very big difference between separable and algebraic closures (in the only case where there is a difference at all, i.e., in positive characteristic $p$). Technically, this com …
Torsten Ekedahl's user avatar
28 votes
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Why are normal crossing divisors nice?

It mostly has to do with finding nice compactifications. Compactifications of varieties are a good thing as they allow us to control what happens at "infinity". If the variety itself is smooth it seem …
12 votes

What is the etymology of the term "perverse sheaf"?

One explanation I heard (it may have been from MacPherson but I am not sure) was that "perverse" was used in the sense of "contrary", the cycles used in the definition refuse to move away from the sin …
Torsten Ekedahl's user avatar