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comment Is every field the field of fractions of an integral domain?
The existence of a prolongation of a valuation to a non algebraic extension field doesn't sem to be mentioned in the standard references (Atiyah, Bourbaki, Matsumura,...). A proof is provided here.
Apr
24
revised When is the tensor product of two fields a field?
added 558 characters in body
Apr
23
awarded  Guru
Apr
22
comment Why considering schemes over discrete valuation rings?
@user54268: sorry, I don't understand your comment. How do you define $R$ and what do you pull-back over $R$ ?
Apr
8
revised What elementary problems can you solve with schemes?
added 186 characters in body
Mar
23
comment Holomorphic line bundles on a punctured disc
@Xander Flood: An algebraic vector bundle may be bon-trivial and have a trivial underlying holomorphic vector bundle.That's exactly what happens with algebraic vector bundles on your punctured elliptic curve.
Mar
18
awarded  Good Answer
Mar
17
comment Embedding of a proper scheme into a smooth one
Thanks for your very clear answer, Francesco: as usual you definitely do not miss anything!
Mar
17
comment Embedding of a proper scheme into a smooth one
How does $D_Y$ give a non-trivial divisor on $X$ ? Couldn't $D_Y$ be disjoint from $X$ ?
Mar
12
awarded  Favorite Question
Mar
2
awarded  Good Answer
Feb
29
awarded  Notable Question
Jan
27
awarded  Great Question
Jan
13
awarded  Nice Answer
Jan
6
awarded  Good Answer
Jan
2
comment Kahler differentials and Ordinary Differentials
@Saal No, it is not right. My experience with n-cafe is that whenever I look up a subject I find clear and elementary they will describe it in such abstract terms that I don't understand what they are talking about. Also, I've never seen them do any non-trivial calculations. But maybe they have done some: I no longer check their site which I find useless for me. But this is very personal. I guess some other mathematicians are enthusiastic about that site: more power to them.
Dec
19
awarded  Good Question
Dec
18
comment Irreducibility of polynomials in two variables
Thanks a lot for the reprint and your fantastic notes, dear Hugo. You write "Nous aimerions maintenant présenter un critère peu connu qui nous garantit qu’un polynôme à plusieurs variables est irréductible" . "Peu connu" indeed! This must be the only elementary algebra course in the universe mentioning Ehrenfeucht's result :-) Congratulations and thank you very much again for teaching us users such beautiful and completely underappreciated mathematics.
Dec
18
comment Irreducibility of polynomials in two variables
Dear viethung, your link sems broken.
Dec
18
awarded  Popular Question