Question

Theorem 7.4.16 (Riemann–Hurwitz formula) in Qing Liu's Algebraic Geometry and Arithmetic Curves

score 265 · Answer 1 · 2026-03-26 21:27:48

265

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Theorem 7.4.16 (Riemann–Hurwitz formula) in Qing Liu's Algebraic Geometry and Arithmetic Curves

Published on 26 Mar 2026 - 21:27

score 67 · Answer 2 · 2021-06-13 23:27:46

67

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Spectrum of localized ring as the germ at a point

Published on 13 Jun 2021 - 23:27

score 91 · Answer 3 · 2026-03-25 12:50:54

91

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If $A_{\overline{k}}\cong \frac{\overline{k}[x]}{(x^p)}$, show that $A\cong \frac{k[x]}{(x^p-c)}$ where $k$ is a field of characteristic $p$

Published on 25 Mar 2026 - 12:50

score 121 · Answer 4 · 2026-03-25 12:50:56

121

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If $A\otimes_R S\cong \frac{S[x]}{(x^p)}$ then $A\cong \frac{R[y]}{(y^p-c)}$ where $R\to S$ is an fppf map

Published on 25 Mar 2026 - 12:50

score 119 · Answer 5 · 2026-04-12 01:09:57

119

Views

Classification of degree 2 scheme over $\mathbb R$

Published on 12 Apr 2026 - 1:09

score 420 · Answer 6 · 2021-06-18 10:46:39

420

Views

Universal property of tensor product and fibre product - how to convert the diagrams

Published on 18 Jun 2021 - 10:46

score 80 · Answer 7 · 2026-03-26 01:12:40

80

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What are the closed subschemes of $\mathbb P^2_R$ for a ring $R$? In particular, what are the closed subschemes of $\mathbb P^2_k$ for a field $k$?

Published on 26 Mar 2026 - 1:12

score 127 · Answer 8 · 2026-04-11 12:49:52

127

Views

Is a pure coherent sheaf locally pure?

Published on 11 Apr 2026 - 12:49

score 67 · Answer 9 · 2026-03-26 23:10:39

67

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If $Z = \operatorname{Supp}\mathscr{F}$ and $\mathscr{I}$ is the sheaf of ideals defined by $Z,$ is it true that $\mathscr{I}\mathscr{F} = 0?$

Published on 26 Mar 2026 - 23:10

score 92 · Answer 10 · 2026-04-09 11:39:07

92

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If $\pi:C\to S$ is a section of an elliptic fibration $f:S\to C$, is $\pi$ a closed immersion?

Published on 09 Apr 2026 - 11:39

score 158 · Answer 11 · 2026-03-28 04:01:47

158

Views

Principal bundles on formal disc and lifting problem

Published on 28 Mar 2026 - 4:01

score 83 · Answer 12 · 2021-06-24 01:30:53

83

Views

Let $X$ be a locally noetherian scheme and let $x\in X$ a point such that $\{x\}$ is locally closed in $X$. Show that dim$\overline{\{x\}}\le1$.

Published on 24 Jun 2021 - 1:30

score 303 · Answer 13 · 2026-03-28 21:06:30

303

Views

Proj of Almost Same Graded Rings are Isomorphic (Exercise from Vakil's FOAG)

Published on 28 Mar 2026 - 21:06

score 209 · Answer 14 · 2026-04-12 22:37:43

209

Views

pullback of line bundle correspond to the fiber product？

Published on 12 Apr 2026 - 22:37

score 108 · Answer 15 · 2026-04-12 20:48:58

108

Views

Suppose $f: X \to Y$ is a separated morphism, $h_1,h_2:T \to X$ induces $h: T \to X \times_Y X$. If $h_1(x) = h_2(x)$ then $h(x) \in \Delta(X)$.

Published on 12 Apr 2026 - 20:48

List Question

Theorem 7.4.16 (Riemann–Hurwitz formula) in Qing Liu's Algebraic Geometry and Arithmetic Curves

Spectrum of localized ring as the germ at a point

If $A_{\overline{k}}\cong \frac{\overline{k}[x]}{(x^p)}$, show that $A\cong \frac{k[x]}{(x^p-c)}$ where $k$ is a field of characteristic $p$

If $A\otimes_R S\cong \frac{S[x]}{(x^p)}$ then $A\cong \frac{R[y]}{(y^p-c)}$ where $R\to S$ is an fppf map

Classification of degree 2 scheme over $\mathbb R$

Universal property of tensor product and fibre product - how to convert the diagrams

What are the closed subschemes of $\mathbb P^2_R$ for a ring $R$? In particular, what are the closed subschemes of $\mathbb P^2_k$ for a field $k$?

Is a pure coherent sheaf locally pure?

If $Z = \operatorname{Supp}\mathscr{F}$ and $\mathscr{I}$ is the sheaf of ideals defined by $Z,$ is it true that $\mathscr{I}\mathscr{F} = 0?$

If $\pi:C\to S$ is a section of an elliptic fibration $f:S\to C$, is $\pi$ a closed immersion?

Principal bundles on formal disc and lifting problem

Let $X$ be a locally noetherian scheme and let $x\in X$ a point such that $\{x\}$ is locally closed in $X$. Show that dim$\overline{\{x\}}\le1$.

Proj of Almost Same Graded Rings are Isomorphic (Exercise from Vakil's FOAG)

pullback of line bundle correspond to the fiber product？

Suppose $f: X \to Y$ is a separated morphism, $h_1,h_2:T \to X$ induces $h: T \to X \times_Y X$. If $h_1(x) = h_2(x)$ then $h(x) \in \Delta(X)$.

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