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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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 …
Dan's user avatar
  • 171
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 …
Dan's user avatar
  • 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 …
Dan's user avatar
  • 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=\ …
Dan's user avatar
  • 171