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Results tagged with ag.algebraic-geometry
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user 57347
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
3
votes
0
answers
298
views
Why define curves over perfect fields?
One may define a curve (e.g. separated scheme of finite type of dim. 1) over an algebraically closed field, as done in Hartshorne's book. A weaker assumption, which is used commonly, is to define a cu …
- 171
2
votes
0
answers
207
views
Is it clear that $y^3=f(x)$ has bad reduction at $3$?
Bad reduction is defined as 'nonexistence' of a model where the curve has good reduction. So let's take the curve $C$ which is affinely given by
$$y^3 = f(x)$$
(absolutely irred, $f$ no multiple roots …
- 171
1
vote
0
answers
140
views
Normalization (integral closure) of $\mathbb Z_p[x]$ in function field of a curve to obtain ...
I want to follow this construction of a normal model of a curve:
Let $p\neq 2,3$ and $Y\to \mathbb P¹$ be a smooth projective curve over $\mathbb Q_p$ with function field $L/\mathbb Q_p(x)$ e.g. $L=\ …
- 171
0
votes
2
answers
327
views
Connection between 'Separated scheme of finite type over spec(k)' and 'Curve in $\mathbb R^n$ [closed]
is there some connection between a curve in the algebraic geometry sense, e.g.
Separated scheme of finite type over spec($k$)
for a field $k$
and a curve in the sense of a smooth map from an in …
- 171