User JBorger

120 votes

How has modern algebraic geometry affected other areas of math?

answered Oct 5, 2011 at 11:58

71 votes

The inverse Galois problem, what is it good for?

nt.number-theory galois-theory

answered Nov 25, 2009 at 1:25

47 votes

Is there a universal property for Witt vectors?

universal-property witt-vectors ra.rings-and-algebras

answered Nov 20, 2009 at 0:37

46 votes

Consequences of not requiring ring homomorphisms to be unital?

ra.rings-and-algebras

answered Aug 3, 2010 at 12:59

41 votes

Accepted

Commutative rings to algebraic spaces in one jump?

ag.algebraic-geometry schemes

answered Jan 9, 2010 at 13:59

37 votes

Accepted

Why are noetherian rings such natural objects in algebraic geometry?

ag.algebraic-geometry soft-question

answered Jul 2, 2011 at 2:39

27 votes

What are some slogans that express mathematical tricks?

soft-question big-picture big-list

answered Sep 26, 2010 at 12:11

22 votes

Why is this not an algebraic space?

ag.algebraic-geometry algebraic-spaces algebraic-groups

answered Dec 15, 2009 at 22:15

20 votes

Problems where we can't make a canonical choice, solved by looking at all choices at once

soft-question big-list

answered Dec 21, 2010 at 20:12

18 votes

Is the moduli space of curves defined over the field with one element?

ag.algebraic-geometry moduli-spaces f-1

answered Jan 4, 2012 at 0:31

16 votes

Accepted

Exact sequence of monoids

semigroups-and-monoids ra.rings-and-algebras short-exact-sequences

answered Dec 9, 2011 at 23:16

15 votes

Accepted

Is an ordinary scheme in Borger's Absolute Geometry the same as a "scheme over F1" with a map to Spec(Z)?

ac.commutative-algebra f-1 lambda-rings

answered Sep 26, 2016 at 10:36

15 votes

Accepted

Applications of algebraic geometry over a field with one element

ag.algebraic-geometry f-1

answered May 4, 2010 at 12:18

14 votes

When and why did the postdoctoral position originate?

ho.history-overview soft-question

answered Mar 2, 2010 at 22:56

14 votes

Precise definition of a scheme (Key question: How to define an open subfunctor without resorting to classical scheme theory)

ag.algebraic-geometry ct.category-theory

answered Feb 8, 2010 at 1:40

14 votes

Why does Neeman avoid t-structures?

reference-request triangulated-categories

answered Aug 13, 2014 at 1:13

14 votes

What's the easiest example of a morphism of topoi that is not from that of a site?

ag.algebraic-geometry sheaf-theory topos-theory

answered Oct 31, 2011 at 8:01

13 votes

Accepted

Is the (regular) inverse Galois problem known for the field C(x,y)?

galois-theory

answered Jun 5, 2010 at 1:20

13 votes

How much of scheme theory can you visualize?

soft-question ag.algebraic-geometry schemes

answered Feb 7, 2010 at 21:26

12 votes

Accepted

Why does the Gamma function satisfy a functional equation?

gamma-function nt.number-theory cohomology motives f-1

answered Feb 6, 2010 at 11:13

12 votes

Accepted

Is every Adams ring morphism a lambda-ring morphism?

lambda-rings adams-operations algebraic-k-theory

answered Jan 31, 2010 at 9:01

12 votes

Accepted

On a Theorem of Fontaine

group-schemes arithmetic-geometry nt.number-theory

answered May 3, 2011 at 7:51

11 votes

Ring with three binary operations

ra.rings-and-algebras

answered May 6, 2013 at 6:05

11 votes

Accepted

Descent of functions along finite birational morphisms

ag.algebraic-geometry ac.commutative-algebra descent

answered Jun 23, 2014 at 8:36

11 votes

Accepted

When is a localization of a commutative ring finitely generated as an algebra?

ac.commutative-algebra

answered Nov 22, 2009 at 9:56

10 votes

Accepted

How to visualize a Witt vector?

ag.algebraic-geometry intuition witt-vectors visualization

answered Jul 16, 2018 at 1:08

9 votes

Accepted

$\lambda$-ring structure defined for a graded ring in Fulton–Lang's book

lambda-rings grothendieck-riemann-roch ac.commutative-algebra ag.algebraic-geometry

answered Sep 30, 2012 at 0:05

9 votes

Are there Néron models over higher dimensional base schemes?

ag.algebraic-geometry nt.number-theory arithmetic-geometry neron-models abelian-varieties

answered Jan 25, 2010 at 20:35

8 votes

Accepted

Endofunctors of CRing which give schemes when composed with schemes?

ag.algebraic-geometry ct.category-theory

answered Feb 3, 2010 at 11:57

8 votes

Criteria for ghost-Witt vectors: looking for history and references

nt.number-theory witt-vectors symmetric-functions co.combinatorics reference-request

answered Apr 15, 2013 at 11:30

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60 Answers

How has modern algebraic geometry affected other areas of math?

The inverse Galois problem, what is it good for?

Is there a universal property for Witt vectors?

Consequences of not requiring ring homomorphisms to be unital?

Commutative rings to algebraic spaces in one jump?

Why are noetherian rings such natural objects in algebraic geometry?

What are some slogans that express mathematical tricks?

Why is this not an algebraic space?

Problems where we can't make a canonical choice, solved by looking at all choices at once

Is the moduli space of curves defined over the field with one element?

Exact sequence of monoids

Is an ordinary scheme in Borger's Absolute Geometry the same as a "scheme over F1" with a map to Spec(Z)?

Applications of algebraic geometry over a field with one element

When and why did the postdoctoral position originate?

Precise definition of a scheme (Key question: How to define an open subfunctor without resorting to classical scheme theory)

Why does Neeman avoid t-structures?

What's the easiest example of a morphism of topoi that is not from that of a site?

Is the (regular) inverse Galois problem known for the field C(x,y)?

How much of scheme theory can you visualize?

Why does the Gamma function satisfy a functional equation?

Is every Adams ring morphism a lambda-ring morphism?

On a Theorem of Fontaine

Ring with three binary operations

Descent of functions along finite birational morphisms

When is a localization of a commutative ring finitely generated as an algebra?

How to visualize a Witt vector?

$\lambda$-ring structure defined for a graded ring in Fulton–Lang's book

Are there Néron models over higher dimensional base schemes?

Endofunctors of CRing which give schemes when composed with schemes?

Criteria for ghost-Witt vectors: looking for history and references