Timeline for Sum of coefficients of a principal divisor

5 events

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Jun 11, 2018 at 0:02	history	edited	Guest	CC BY-SA 4.0	added 93 characters in body
Jun 10, 2018 at 23:43	comment	added	Guest		Thanks! I proved this fact in a strange way; I use base change to $\mathbb{C}$ by making use of embeddings $K\rightarrow \mathbb{C}$. Then $\sum d_{i}dm_{i}$ is actually the sum of zeros and poles of $f$ on $X\otimes_{\mathbb{C}}$. Since $f\in K(X)$ the sum must be zero. I never heard of the notation of "generic divisor". Thanks for the hint and the help.
Jun 10, 2018 at 19:43	comment	added	Noam D. Elkies		(Which means that it's actually $\sum_i d_i m_i = 0$, where $m_i$ is the "intersection multiplicity of $D_i$ with the generic fiber"; in more concrete language, $X$ is a curve over some number field $K$, and each $D_i$ is a point defined over some degree $m_i$ extension of $K$.)
Jun 10, 2018 at 2:57	comment	added	Noam D. Elkies		Look on the generic divisor. (In down-to-earth language: it comes down to "#zeros = #poles" on an algebraic curve.)
Jun 9, 2018 at 21:58	history	asked	Guest	CC BY-SA 4.0