180 What elementary problems can you solve with schemes? 2011-03-21T15:48:21.763

158 What should be learned in a first serious schemes course? 2010-06-17T12:49:42.873

43 Connections between various generalized algebraic geometries (Toen-Vaquié, Durov, Diers, Lurie)? 2012-02-25T10:26:56.037

42 Why "open immersion" rather than "open embedding"? 2010-12-07T02:53:57.313

38 A closed subscheme of an open subscheme that is not an open subscheme of a closed subscheme? 2010-01-28T15:13:02.010

35 Arbitrary products of schemes don't exist, do they? 2009-12-16T22:09:20.507

33 Ring-theoretic characterization of open affines? 2010-04-08T21:10:26.853

31 Commutative rings to algebraic spaces in one jump? 2010-01-09T10:11:57.903

31 What is the inverse image sheaf necessary for in algebraic geometry? 2010-09-30T15:42:46.143

31 Useful, non-trivial general theorems about morphisms of schemes 2016-03-24T23:56:01.030

29 Mikhalkin's tropical schemes versus Durov's tropical schemes 2011-08-10T19:19:58.050

28 How much of scheme theory can you visualize? 2010-02-07T05:12:08.077

26 Spectrum of the Grothendieck ring of varieties 2009-10-11T22:10:05.750

24 The Frobenius morphism 2010-12-20T19:46:51.203

23 A book on locally ringed spaces? 2010-02-01T02:33:46.693

23 Categorical construction of the category of schemes? 2010-05-30T21:21:36.570

22 Reduced scheme and closed points 2010-01-17T16:12:09.503

22 Reference for de Rham cohomology in positive characteristic 2015-10-31T20:38:55.047

21 Intuition behind generic points in a scheme 2012-02-24T05:39:05.770

20 Why and how did preschemes become schemes? 2011-02-16T16:26:59.057

20 Why would one "attempt" to define points of a motive as $\operatorname{Ext}^1(\mathbb{Q}(0),M)$? 2015-09-28T00:34:04.267

19 When is an irreducible scheme quasi-compact? 2010-08-05T12:55:59.907

19 Does Zariski's Main Theorem come with a canonical factorization? 2011-02-18T21:14:03.413

18 Extending vector bundles on a given open subscheme 2010-04-21T20:28:09.383

18 Does every relative curve have a Picard scheme? 2014-11-10T13:46:22.177

17 What are the Benefits of Using Algebraic Spaces over Schemes? 2009-10-29T02:40:29.263

17 What are the epimorphisms in the category of schemes? 2011-02-24T21:19:10.907

17 Geometric generic fibre 2015-07-05T14:34:39.500

17 History of the functor of points 2016-01-13T16:47:14.007

17 Can $\mathcal O_X$ be recognized abstract-nonsensically? 2016-12-09T05:37:32.250

16 What is an explicit example of a variety X which is finite over Spec F_p but which does not lift to a scheme Y which is finite and flat over Spec Z_p? 2011-05-05T02:59:02.313

16 Homotopy types of schemes 2015-09-10T18:32:02.000

16 A book on elliptic curves using scheme theory? 2017-04-05T16:03:04.313

15 Functorial characterization of open subschemes? 2009-10-20T03:49:51.093

15 Construction of the petit Zariski topos out of the gros topos of a scheme 2010-04-07T11:43:52.463

15 Universal homeomorphisms and the étale topology 2010-11-24T09:11:51.633

15 What are the monomorphisms in the category of schemes? 2011-02-25T03:23:36.123

15 Minimal number of generators for $A^n$ 2012-11-17T10:20:36.180

14 Is there an example of a variety over the complex numbers with no embedding into a smooth variety? 2009-10-08T15:42:30.050

14 Affine scheme on spec(A) of a ring A as the sheafification of a pre-sheave on spec(A)? 2011-11-10T02:58:37.963

12 Is there an example of a formally smooth morphism which is not smooth? 2009-10-08T12:06:56.370

12 Constructing a degeneration (as a group scheme) of G_m to G_a 2009-11-03T07:07:22.837

12 Non-simply-connected smooth proper scheme over Z? 2010-01-07T20:48:46.613

12 Closed vs Rational Points on Schemes 2010-02-02T22:51:59.597

12 Infinite projective space 2010-03-30T03:37:01.003

12 Images and Monomorphisms of Schemes 2010-03-30T19:38:04.160

12 Extending properties of commutative rings to schemes 2010-05-12T03:58:36.177

12 Classical algebraic varieties VS $k$-schemes VS schemes 2014-02-18T21:00:19.367

12 Are all formal schemes *really* Ind-schemes? 2016-04-15T19:54:53.603

11 Nonalgebraic complex varieties 2010-01-29T19:13:16.653

11 What is the difference between Grothendieck groups K_0(X) vs K^0(X) on schemes? 2010-04-21T21:34:51.703

11 Replacing Spectrum with Valuations of a Field - An Alternative to Schemes? 2010-07-21T20:20:28.060

11 Which local ringed spaces are schemes? 2012-12-10T21:35:12.503

11 Obstructed automorphisms of schemes 2016-02-05T14:24:58.183

11 Sheaf associated to presheaf Aut 2017-02-08T22:45:30.690

11 Idea behind Grothendieck's proof that formally smooth implies flat? 2017-12-10T23:54:41.677

10 How does descent theory imply a sheaf is a scheme? 2012-11-20T22:38:40.563

10 On representable abelian sheaves vs abelian sheaves 2018-01-13T09:06:42.650

9 Can one check formal smoothness using only one-variable Artin rings? 2009-10-06T12:14:36.740

9 Can an algebraic space fail to have a unviersal map to a scheme? 2009-11-08T03:58:20.253

9 Can a scheme be defined by gluing open affines such that the intersections are affine? 2010-07-12T13:46:27.610

9 explanation on a scheme which is not affine scheme 2012-02-03T21:39:05.547

9 Is there a direct proof that affine schemes are fppf quasi-compact? 2013-03-19T09:08:54.710

9 Is the category of schemes wellpowered? regularly wellpowered? 2014-03-17T19:43:22.170

9 on the local structure of schemes 2015-01-17T12:55:35.723

9 Is the functor of points of a scheme cofinally small? 2015-01-19T07:51:09.273

9 Weierstrass division theorem for henselian rings 2015-02-23T09:44:42.227

9 Torsors trivializing over a fixed finite etale cover 2015-07-15T15:48:43.807

9 Isomorphic schemes over DVR 2016-11-27T02:31:55.157

8 The category of finite locally-free commutative group schemes 2009-12-03T17:27:33.660

8 Is this finite surjective flat morphism of 2 dimensional schemes a local complete intersection 2010-10-03T15:53:07.023

8 pushforward of locally free sheaf is locally free? 2011-09-27T21:44:43.150

8 Jacobian criterion for smoothness of schemes 2011-11-03T18:09:13.173

8 Nonnegative additive functions on coherent sheaves 2011-12-13T04:40:28.347

8 Do Disjoint Unions and Fiber Products Commute? 2012-02-24T20:52:53.580

8 What about schemes built up out of graded rings? 2013-03-14T01:00:22.010

8 About the relation between the categories $\text{Sch}$, $\text{LRS}$ and $\text{RS}$ 2015-08-31T14:14:44.653

8 Parahoric Group Scheme 2015-09-11T09:49:52.650

8 Are there varieties with non finitely generated Picard group and vanishing irregularity? 2015-11-02T12:41:28.510

8 Base schemes and Bayesian priors 2015-11-17T01:04:45.410

8 Arithmetic zeta function and local zeta functions 2015-11-19T16:09:11.947

8 Tube of a mod p point on a smooth Z_(p)-scheme 2016-03-22T20:00:16.197

8 Can the algebraic geometry of schemes be developed internally in topoi? 2016-12-03T05:51:48.750

7 Functorial characterization of morphisms of schemes 2010-02-16T17:10:41.377

7 Diagonal map and "infinitesimal points" 2011-02-07T01:55:36.180

7 Scheme-theoretic account of why every variety embeds in a complete variety 2011-03-01T00:36:26.807

7 Complex analytic space with no (positive dim.) subscheme ? 2011-05-08T12:53:07.963

7 Closed points of valuation scheme 2011-05-21T21:30:20.363

7 Proper morphism sending coherent to coherent 2011-12-06T13:31:03.117

7 Two definitions of smoothness? 2012-09-15T17:48:14.950

7 (Mixed) Tate motives 2012-10-26T14:11:28.127

7 Evaluation maps for moduli of stable maps 2015-03-23T21:34:36.630

7 Higher-dimensional Artin L-functions 2015-10-15T09:05:25.373

7 A Hartogs-type criterion for flatness 2016-04-19T17:22:06.253

7 Archimedean fibers "intersecting" curves on arithmetic surfaces 2016-05-08T14:56:32.367

7 $\Bbb A^1$-Localisation of Schemes, and $\Bbb A^1$-Rigid Schemes 2016-05-26T04:40:36.443

7 When are free modules on sheaves of sets quasicoherent? 2017-03-04T09:47:53.750

7 universally open and connected fibers 2018-01-26T18:41:47.253

6 When is the push-forward of the structure sheaf locally free 2010-05-07T20:13:50.220