User user2146

885

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269

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242k

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Examples of common false beliefs in mathematics

big-list mathematics-education

Feb 10 at 16:12 José Hdz. Stgo. 7,300

351

votes

22

answers

52k

views

Thinking and Explaining

soft-question ho.history-overview big-list big-picture math-communication

Sep 2 at 11:29 Mozibur Ullah 1,095

242

votes

41

answers

87k

views

A single paper everyone should read? [closed]

soft-question big-list

Apr 16 at 15:27 Community♦ 1

69

votes

2

answers

6k

views

The inverse Galois problem and the Monster

gr.group-theory galois-theory nt.number-theory ag.algebraic-geometry

Dec 29 '19 at 10:18 WhatsUp 2,990

69

votes

6

answers

5k

views

Rigidity of the category of schemes

ag.algebraic-geometry ct.category-theory

Dec 23 '19 at 21:10 Community♦ 1

53

votes

7

answers

5k

views

Are higher categories useful?

higher-category-theory big-list

Dec 11 '11 at 15:42 Dmitri Pavlov 22.9k

47

votes

6

answers

6k

views

Colimits of schemes

ag.algebraic-geometry

Jul 14 at 17:42 Ben Lim 1,610

41

votes

7

answers

8k

views

Non-examples of model structures, that fail for subtle/surprising reasons?

ct.category-theory at.algebraic-topology model-categories homotopy-theory higher-category-theory

Jul 27 '17 at 19:44 David White 20.6k

38

votes

4

answers

2k

views

Pre-triangulated category that isn't triangulated

ct.category-theory triangulated-categories reference-request

Mar 7 '17 at 0:50 motivique 57

35

votes

9

answers

4k

views

Computing fundamental groups and singular cohomology of projective varieties

ag.algebraic-geometry at.algebraic-topology

Jul 19 '18 at 20:39 j.c. 12.7k

32

votes

3

answers

2k

views

For which spaces is homology (or cohomology) determined by the Eilenberg-Steenrod axioms

homotopy-theory homology shape-theory

Oct 29 '09 at 17:09 Community♦ 1

29

votes

3

answers

3k

views

Sheaf description of $G$-bundles

ag.algebraic-geometry sheaf-theory principal-bundles

Nov 29 '19 at 15:53 YCor 42.6k

24

votes

4

answers

3k

views

(∞, 1)-categorical description of equivariant homotopy theory

homotopy-theory infinity-categories ct.category-theory at.algebraic-topology equivariant-homotopy

Nov 17 '09 at 18:13 Mark Hovey 3,325

22

votes

3

answers

3k

views

Homotopy theory of schemes examples

ag.algebraic-geometry homotopy-theory motivic-cohomology

Jan 21 '10 at 21:30 Denis-Charles Cisinski 9,806

22

votes

4

answers

2k

views

A Peculiar Model Structure on Simplicial Sets?

at.algebraic-topology simplicial-stuff model-categories homological-algebra

Feb 8 '10 at 1:22 Community♦ 1

22

votes

1

answer

3k

views

Voevodsky's counterexample to the existence of a motivic t-structure

ag.algebraic-geometry kt.k-theory-and-homology motives motivic-homotopy

May 25 '17 at 4:53 David White 20.6k

21

votes

0

answers

1k

views

What is the current knowledge of equivariant cohomology operations?

at.algebraic-topology equivariant-homotopy motivic-cohomology

Apr 18 '10 at 15:02 Bill Kronholm 815

19

votes

1

answer

1k

views

What's coherent about coherent sheaves?

terminology ho.history-overview reference-request

Oct 29 '10 at 18:28 Community♦ 1

18

votes

3

answers

2k

views

What are the fibrant objects in the injective model structure?

homotopy-theory at.algebraic-topology simplicial-stuff model-categories

Jul 2 '15 at 7:15 Community♦ 1

16

votes

6

answers

2k

views

Can any topological space be the result of a scheme?

gn.general-topology ag.algebraic-geometry

Jul 31 '10 at 15:26 Pete L. Clark 60.5k

15

votes

4

answers

2k

views

Relation between motivic homotopy category and the derived category of motives

motivic-cohomology motivic-homotopy ag.algebraic-geometry

May 3 '16 at 16:50 Thi 216

13

votes

3

answers

3k

views

The Yoneda Lemma for $(\infty,1)$-categories?

ct.category-theory higher-category-theory infinity-categories yoneda-lemma

Jan 22 '19 at 14:01 Martin Sleziak 4,232

13

votes

3

answers

1k

views

What are the endofunctors on the simplex category?

simplicial-stuff

Jun 10 '10 at 16:48 Tom Goodwillie 45.9k

8

votes

0

answers

617

views

Finite generation of equivariant cohomology rings

at.algebraic-topology equivariant-cohomology

Feb 28 '12 at 11:55 Mark Grant 30.9k

7

votes

2

answers

254

views

What are the fibres of a representable simplicial sheaf (in the Nisnevich topology)

ag.algebraic-geometry ct.category-theory at.algebraic-topology

Nov 18 '09 at 3:45 Luis 51

6

votes

3

answers

2k

views

categorical homotopy colimits

homotopy-theory at.algebraic-topology

Jan 1 '10 at 21:48 Martin Brandenburg 53.2k

6

votes

1

answer

1k

views

Line bundles: from transition functions to divisors

ag.algebraic-geometry line-bundles

Feb 27 '10 at 15:06 Pavel Etingof 3,709

4

votes

1

answer

751

views

references for models of stable infinity categories

higher-category-theory homotopy-theory ct.category-theory at.algebraic-topology

Jan 21 '10 at 2:09 Chris Schommer-Pries 23.6k

4

votes

1

answer

539

views

Sheaf condition and representability in the category Top

sheaf-theory representable-functors gn.general-topology ag.algebraic-geometry

May 10 '10 at 17:49 Community♦ 1

2

votes

1

answer

350

views

Homotopy equivalent spaces and $G_m$-actions

ag.algebraic-geometry at.algebraic-topology

Apr 24 '12 at 11:15 Francesco 371

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Examples of common false beliefs in mathematics

Thinking and Explaining

A single paper everyone should read? [closed]

The inverse Galois problem and the Monster

Rigidity of the category of schemes

Are higher categories useful?

Colimits of schemes

Non-examples of model structures, that fail for subtle/surprising reasons?

Pre-triangulated category that isn't triangulated

Computing fundamental groups and singular cohomology of projective varieties

For which spaces is homology (or cohomology) determined by the Eilenberg-Steenrod axioms

Sheaf description of $G$-bundles

(∞, 1)-categorical description of equivariant homotopy theory

Homotopy theory of schemes examples

A Peculiar Model Structure on Simplicial Sets?

Voevodsky's counterexample to the existence of a motivic t-structure

What is the current knowledge of equivariant cohomology operations?

What's coherent about coherent sheaves?

What are the fibrant objects in the injective model structure?

Can any topological space be the result of a scheme?

Relation between motivic homotopy category and the derived category of motives

The Yoneda Lemma for $(\infty,1)$-categories?

What are the endofunctors on the simplex category?

Finite generation of equivariant cohomology rings

What are the fibres of a representable simplicial sheaf (in the Nisnevich topology)

categorical homotopy colimits

Line bundles: from transition functions to divisors

references for models of stable infinity categories

Sheaf condition and representability in the category Top

Homotopy equivalent spaces and $G_m$-actions