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Answers
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10
Example of codim 1 regular embedding that is not an effective Cartier divisor?
8
morphism between two elliptic curves over a local field
2
Dimension of formal fiber
5
Open idempotents in modules over a local ring
7
Which schemes can be presented as limits of smooth varieties?
5
Artin approximation theorems over non-regular rings/non-Noetherian rings
9
Are noetherian schemes generically Jacobson?
5
purity for finite flat group schemes
8
Are rational varieties simply connected?
6
Representability of sheaf of Ext^1 of a Néron model by $\mathbb{G}_m$
6
Over which fields does the Mordell-Weil theorem hold?
18
An etale version of the van Kampen theorem
15
Is every algebraic space the quotient of a scheme by a finite group?
1
Irreducible “family” of relative effective divisors of a smooth morphism
3
is intersection of a curve and a family of curves generically constant as a scheme?
4
Decomposition of a proper morphism
6
non-isomorphic stably isomorphic fields
3
Is reflexivity an open condition?
6
finite non-commutative local group schemes
12
What are some examples of ingenious, unexpected constructions?
5
Categorical interpretation of quasi-compact quasi-separated schemes
2
In what sense is a generically submersive morphism of varieties subermersive over singular points?
3
Spreading out of flat morphisms of schemes
7
Do Disjoint Unions and Fiber Products Commute?
5
Rigidity of the category of schemes
1
is a cartesian square of a group scheme with $\mathbb{G}_a^n$ fibres reduced?
3
sections of very ample line bundle
2
Relative generic flatness.
4
Etale group schemes over a local ring
11
Number of affines needed to cover a variety
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