User James D. Taylor

9 votes

1 answer

705 views

What is the motivation for defining the conductor of an abelian variety?

asked Dec 22, 2013 at 2:46

16 votes

1 answer

1k views

How can one interpret homology and Stokes' Theorem via derived categories?

asked Jun 23, 2013 at 19:17

7 votes

2 answers

1k views

Is there a nice criterion for when the splitting fields of two irreducible polynomials are equal?

asked Apr 3, 2013 at 19:02

3 votes

1 answer

597 views

Why is there no "regular etale fundamental group"?

asked Oct 4, 2012 at 16:03

293 votes

8 answers

141k views

Philosophy behind Mochizuki's work on the ABC conjecture

asked Sep 7, 2012 at 1:06

12 votes

0 answers

876 views

What is the intuition for $\mathbb{Q}^{ab}$ having cohomological dimension $1$?

asked May 15, 2012 at 20:57

3 votes

1 answer

309 views

Are there n polynomials for which all intersection multiplicities are at least m?

asked Feb 12, 2012 at 17:56

5 votes

4 answers

517 views

What is the obstruction for a local set of models of a curve to come from a global model?

asked Jan 25, 2012 at 23:48

5 votes

1 answer

1k views

Where was Riemann Existence first proven?

asked Dec 10, 2011 at 19:48

2 votes

0 answers

382 views

General cohomology groups and motives

asked Nov 23, 2011 at 22:51

47 votes

1 answer

2k views

Did Grothendieck have a plan for proving Riemann Existence algebraically?

asked Nov 13, 2011 at 0:27

3 votes

2 answers

419 views

Does a curve have infinitely many $K$-rational points under these hypotheses?

asked Oct 31, 2011 at 0:15

5 votes

1 answer

1k views

In what way do the Weil Conjectures pertain to Langlands?

asked Oct 25, 2011 at 19:43

2 votes

1 answer

621 views

What are non-abelian $L$-functions?

asked Oct 23, 2011 at 21:31

72 votes

5 answers

8k views

Is there an intuitive reason for Zariski's main theorem?

asked Oct 20, 2011 at 19:21

9 votes

3 answers

848 views

Is there a connected non-affine scheme $S$ such that it is the union of rings of integers of number fields?

asked Sep 25, 2011 at 17:41

12 votes

2 answers

3k views

What is the non-motivic motivation behind automorphic representations?

asked Sep 17, 2011 at 23:58

14 votes

5 answers

3k views

What is the "reason" for modularity results?

asked Sep 13, 2011 at 17:18

3 votes

1 answer

1k views

What is the interpretation of complex multiplication in terms of Langlands?

asked Sep 7, 2011 at 18:05

10 votes

1 answer

2k views

How does the conjectural Langlands group fit into the Tannakian point of view?

asked Sep 7, 2011 at 0:48

2 votes

2 answers

915 views

Are the $L$-functions of $X_0(N)$ automorphic?

asked Sep 3, 2011 at 18:23

14 votes

2 answers

2k views

How would a motivic proof of the Riemann hypothesis over finite fields go?

asked Aug 14, 2011 at 16:51

3 votes

1 answer

759 views

Is the "L-function of the complex cohomology" of a motive equal to the L-function of its l-adic realization?

asked Aug 10, 2011 at 4:31

3 votes

0 answers

365 views

Is there a notion of a zeta function of a morphism?

asked Aug 9, 2011 at 17:07

1 vote

0 answers

296 views

(why) Are the following two constructions of zeta functions equal?

asked Aug 9, 2011 at 0:58

11 votes

2 answers

2k views

What is the strongest, most natural, conjectural form of Langlands?

asked Aug 2, 2011 at 23:33

23 votes

1 answer

3k views

What is the precise relationship between Langlands and Tannakian formalism?

asked Jul 31, 2011 at 17:38

8 votes

2 answers

1k views

Is there a ``path'' between any two fiber functors over the same field in Tannakian formalism?

asked Jul 31, 2011 at 15:46

23 votes

2 answers

2k views

Why would the category of Motives be Tannakian?

asked Jul 30, 2011 at 16:16

19 votes

2 answers

3k views

What are the different theories that the motivic fundamental group attempts to unify?

asked Jul 29, 2011 at 16:20

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65 Questions

What is the motivation for defining the conductor of an abelian variety?

How can one interpret homology and Stokes' Theorem via derived categories?

Is there a nice criterion for when the splitting fields of two irreducible polynomials are equal?

Why is there no "regular etale fundamental group"?

Philosophy behind Mochizuki's work on the ABC conjecture

What is the intuition for $\mathbb{Q}^{ab}$ having cohomological dimension $1$?

Are there n polynomials for which all intersection multiplicities are at least m?

What is the obstruction for a local set of models of a curve to come from a global model?

Where was Riemann Existence first proven?

General cohomology groups and motives

Did Grothendieck have a plan for proving Riemann Existence algebraically?

Does a curve have infinitely many $K$-rational points under these hypotheses?

In what way do the Weil Conjectures pertain to Langlands?

What are non-abelian $L$-functions?

Is there an intuitive reason for Zariski's main theorem?

Is there a connected non-affine scheme $S$ such that it is the union of rings of integers of number fields?

What is the non-motivic motivation behind automorphic representations?

What is the "reason" for modularity results?

What is the interpretation of complex multiplication in terms of Langlands?

How does the conjectural Langlands group fit into the Tannakian point of view?

Are the $L$-functions of $X_0(N)$ automorphic?

How would a motivic proof of the Riemann hypothesis over finite fields go?

Is the "L-function of the complex cohomology" of a motive equal to the L-function of its l-adic realization?

Is there a notion of a zeta function of a morphism?

(why) Are the following two constructions of zeta functions equal?

What is the strongest, most natural, conjectural form of Langlands?

What is the precise relationship between Langlands and Tannakian formalism?

Is there a ``path'' between any two fiber functors over the same field in Tannakian formalism?

Why would the category of Motives be Tannakian?

What are the different theories that the motivic fundamental group attempts to unify?