Johan’s question seminar

Check out my ongoing write-up for an informal seminar. The theme of this seminar is that participants ask some little easy question which is somewhat fun and then we vote meet once a week to solve one or two of them. The reason to do so is to “make sure everyone get out of their bed once a week”.

I didn’t write down all the discussions of questions, due to my lack of attention, patience and time. Here are the questions of which I’ve written down some discussions:

(1) Given an étale map between varieties with constant number of fibers, is it necessarily a finite étale map?

(2) Is a quotient of locally ringed space by a finite group action always a locally ringed space?

(3) Why is there no section from PGL_n to GL_n?

(4) Is it true that any small perturbation of a diagonalizable matrix in GL_n(Z_p) with distinct eigenvalues diagonalizable? (Note that here diagonalization should happen within Z_p)

(5) How many lines of the 27 on a REAL cubic surface real (what are the possibilities)?

In the following weeks I will keep writing down further discussions of other fun little questions (hopefully), so check out the link above later~

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