Reputation
1,537
Next privilege 2,000 Rep.
Edit questions and answers
Badges
3 16 40
Impact
~73k people reached

17h
comment Incipit of chapter VI of Neukirch's ANT book.
I've seen the chapter that you mention. You are right, and moreover it seems that the definition is the same
1d
asked Incipit of chapter VI of Neukirch's ANT book.
Feb
8
comment Fixed fields in Neukirch's book (chap. IV): notational problem
Yes, I think you are right. It is the most reasonable explanation.
Feb
8
asked Fixed fields in Neukirch's book (chap. IV): notational problem
Feb
6
accepted homomorphism of profinite groups
Feb
6
comment homomorphism of profinite groups
How can I prove that the open subgroups (=of finite index) of $\widehat{\mathbb Z}$ are of the type $m\widehat{\mathbb Z}$
Feb
6
asked homomorphism of profinite groups
Feb
1
comment Valuation ring between $F$ and $\mathcal O_F$
I think that the correct equation is $\omega^{-1}=u^{-1}\omega^{-k-1}x$
Feb
1
accepted Valuation ring between $F$ and $\mathcal O_F$
Feb
1
revised Valuation ring between $F$ and $\mathcal O_F$
added 40 characters in body
Feb
1
asked Valuation ring between $F$ and $\mathcal O_F$
Jan
31
accepted Function field on a non-singular algebraic curve as the field of meromorphic functions
Jan
31
accepted Restricted valuation on subring of a DVR
Jan
31
comment Restricted valuation on subring of a DVR
Of course! A valuation ring the "set" of ALL elements with non negative valuation. Thank you.
Jan
31
asked Restricted valuation on subring of a DVR
Jan
28
comment Function field on a non-singular algebraic curve as the field of meromorphic functions
This is a good point. Thank you.
Jan
27
comment Function field on a non-singular algebraic curve as the field of meromorphic functions
Yes, there is not a complete answer for this question. Anyone is free to define his own meromorphic functions. I'm only trying to see which are the most natural analogies between the world of manifolds and the world of algebraic varieties. This site contains plenty of people that generally are able to give very inspiring hints, so that's the reason of my "question".
Jan
27
comment Function field on a non-singular algebraic curve as the field of meromorphic functions
That's true! but we lose the power series expansion
Jan
27
comment Function field on a non-singular algebraic curve as the field of meromorphic functions
Moreover: you are right! For every (closed) point I have a discrete valuation so for every Laurent expansion I have to chance valuation. On the other hand, note that $k(X)=\text{Frac}(\mathcal O_X(X)) $ , and on compact Rieman surfaces the field of meromorphic functions is not the field of fractions of holomorphic functions. So, I continue to believe that the analogy is wrong.
Jan
27
comment Function field on a non-singular algebraic curve as the field of meromorphic functions
Yes of course I mean d.v. ring.