User Mikhail Bondarko

57 votes

13 answers

20k views

'Important' applications of p-adic numbers outside of algebra (and number theory).

asked Dec 26, 2011 at 16:17

26 votes

0 answers

1k views

The most important facts, modern surveys, and readable introductions to p-adic cohomology theories (crystalline cohomology and the mysterious functor)

asked Feb 14, 2014 at 9:10

25 votes

2 answers

3k views

Most significant results in motivic integration theory?

asked Aug 19, 2013 at 9:16

23 votes

1 answer

1k views

Is hyperelliptic cryptography "practical"?

asked Feb 1, 2016 at 17:51

20 votes

1 answer

2k views

Any algebraic substitute for Morse theory (and homology) in arbitrary characteristic?

asked Oct 9, 2012 at 9:09

18 votes

1 answer

1k views

Which motivic cohomology groups of complex numbers are non-torsion?

asked May 9, 2017 at 11:39

17 votes

1 answer

7k views

A nice explanation of what is a smooth (l-adic) sheaf?

asked Jul 19, 2010 at 12:31

15 votes

1 answer

2k views

What is the purpose of section 3 of BBD?

asked Apr 11, 2013 at 19:05

15 votes

1 answer

527 views

What are the advantages of various "models" for the motivic stable homotopy category

asked Apr 25, 2017 at 22:27

15 votes

2 answers

5k views

What areas of algebra could be interesting to probability theorists?

asked Dec 5, 2016 at 23:08

14 votes

1 answer

746 views

Can there exist Chow motives/motivic cohomology for compact Kähler manifolds?

asked Nov 3, 2012 at 8:57

14 votes

1 answer

1k views

Motivic cohomology vs. K-theory for singular varieties

asked Feb 1, 2012 at 17:53

14 votes

1 answer

2k views

On polarized (pure) Hodge structures

asked Oct 13, 2010 at 10:16

14 votes

1 answer

1k views

Are two conjectural descriptions of the motivic t-structure (via cohomology and via affine varieties) known to be equivalent?

asked Jan 26, 2011 at 17:22

13 votes

4 answers

2k views

Localizing an arbitrary additive category

asked Oct 29, 2010 at 2:30

13 votes

1 answer

591 views

Is there a yoga of effectivity for motives and their realizations?

asked May 31, 2014 at 10:46

12 votes

1 answer

551 views

Presenting $\mathbb{Q}[[t]]$ as an explicit colimit of smooth $\mathbb{Q}$-algebras: an explicit example for the Popescu's theorem

asked Jan 21, 2014 at 5:53

12 votes

1 answer

403 views

Which statements and arguments of Hovey's "Model categories" fail without functorial factorizations of morphisms?

asked Nov 30, 2013 at 13:54

12 votes

3 answers

3k views

Derived categories of (coherent) sheaves of modules: exceptional images, gluing, and proper descent?

asked May 27, 2011 at 10:07

11 votes

2 answers

1k views

The vanishing of $MGL^{2n+i,n}(X)$; do spectra of smooth projective varieties generate $SH_{l}$?

asked Nov 8, 2012 at 20:53

11 votes

2 answers

728 views

Do there exist "topologically significant" (and not "algebraic") triangulated categories killed by the multiplication by $p$?

asked Sep 17, 2015 at 14:21

11 votes

1 answer

266 views

What are the projective dimensions of big fraction fields?

asked Nov 20, 2019 at 19:11

11 votes

1 answer

1k views

Is it fine to correct and extend texts of a late colleague when publishing them?

asked Mar 13 at 9:36

10 votes

1 answer

1k views

Bad behaviour of perverse sheaves over 'general' bases?

asked Feb 17, 2011 at 22:45

10 votes

2 answers

567 views

Does a triangulated category that possesses a subcategory $B$ of generators with no extensions of non-zero degree between them have to be isomorphic to $K^b(B)$?

asked Dec 1, 2010 at 6:01

9 votes

2 answers

583 views

Can one ignore primes lying over $l$ in the Fontaine-Mazur conjecture? Counterexamples?

asked Oct 21, 2012 at 22:08

9 votes

3 answers

2k views

Applications for intersection (co)homology and for the Decomposition Theorem for students?

asked Feb 16, 2013 at 16:24

9 votes

0 answers

336 views

Is it possible to define a perverse $t$-structure for a certain triangulated category of sheaves of spectra?

asked Mar 1, 2012 at 11:32

9 votes

1 answer

934 views

The vanishing of non-connective K-theory in negative degrees

asked Sep 1, 2011 at 7:03

9 votes

1 answer

923 views

Is the functor from the unbounded derived category of coherent sheaves into the derived category of quasi-coherent sheaves fully faithful?

asked Mar 26, 2023 at 16:27

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274 Questions

'Important' applications of p-adic numbers outside of algebra (and number theory).

The most important facts, modern surveys, and readable introductions to p-adic cohomology theories (crystalline cohomology and the mysterious functor)

Most significant results in motivic integration theory?

Is hyperelliptic cryptography "practical"?

Any algebraic substitute for Morse theory (and homology) in arbitrary characteristic?

Which motivic cohomology groups of complex numbers are non-torsion?

A nice explanation of what is a smooth (l-adic) sheaf?

What is the purpose of section 3 of BBD?

What are the advantages of various "models" for the motivic stable homotopy category

What areas of algebra could be interesting to probability theorists?

Can there exist Chow motives/motivic cohomology for compact Kähler manifolds?

Motivic cohomology vs. K-theory for singular varieties

On polarized (pure) Hodge structures

Are two conjectural descriptions of the motivic t-structure (via cohomology and via affine varieties) known to be equivalent?

Localizing an arbitrary additive category

Is there a yoga of effectivity for motives and their realizations?

Presenting $\mathbb{Q}[[t]]$ as an explicit colimit of smooth $\mathbb{Q}$-algebras: an explicit example for the Popescu's theorem

Which statements and arguments of Hovey's "Model categories" fail without functorial factorizations of morphisms?

Derived categories of (coherent) sheaves of modules: exceptional images, gluing, and proper descent?

The vanishing of $MGL^{2n+i,n}(X)$; do spectra of smooth projective varieties generate $SH_{l}$?

Do there exist "topologically significant" (and not "algebraic") triangulated categories killed by the multiplication by $p$?

What are the projective dimensions of big fraction fields?

Is it fine to correct and extend texts of a late colleague when publishing them?

Bad behaviour of perverse sheaves over 'general' bases?

Does a triangulated category that possesses a subcategory $B$ of generators with no extensions of non-zero degree between them have to be isomorphic to $K^b(B)$?

Can one ignore primes lying over $l$ in the Fontaine-Mazur conjecture? Counterexamples?

Applications for intersection (co)homology and for the Decomposition Theorem for students?

Is it possible to define a perverse $t$-structure for a certain triangulated category of sheaves of spectra?

The vanishing of non-connective K-theory in negative degrees

Is the functor from the unbounded derived category of coherent sheaves into the derived category of quasi-coherent sheaves fully faithful?