32 Are submersions of differentiable manifolds flat morphisms? 2009-10-19T14:16:35.740

30 Flatness in Algebraic Geometry vs. Fibration in Topology 2010-04-02T19:47:22.783

20 Can a quotient ring R/J ever be flat over R? 2009-10-08T22:18:19.433

19 Homotopy flat DG-modules 2010-09-26T16:53:57.713

18 Does projective imply flat? 2015-06-30T16:15:31.290

13 Every finitely generated flat module over a ring with finitely many minimal primes is projective 2015-09-19T23:30:29.363

12 Does smoothness descend along flat morphisms? 2012-02-22T01:06:16.107

11 Given a family of curves, when does there exist a fibered surface over Spec Z parametrizing them? 2011-02-04T10:34:21.850

11 Is there a notion of "flat vector bundle over a topological space"? 2015-09-28T02:03:52.310

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

10 intuition about the "section after base-change" for flat descent and exactness of the Amitsur complex 2009-11-29T19:35:29.997

10 Relationship between monodromy representations and isomorphism of flat vector bundles 2012-03-26T13:11:40.483

9 Associated graded and flatness 2010-07-27T16:34:33.273

9 Resolution of singularities for flat families. 2012-02-09T15:38:32.087

9 Can flatness be specified by a natural coherent sheaf? 2012-09-07T20:53:16.140

9 flatness of power series rings 2013-01-31T12:33:38.713

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

9 Homotopical interpretation of flatness? 2016-06-22T10:05:55.863

9 Flatness from constancy of dimension of fibers 2017-01-14T09:50:42.683

8 When can one extend a flat family from a subscheme to the whole scheme? 2010-09-30T18:03:50.227

7 Extending faithfully flat covers of closed subschemes to open neighborhoods 2011-12-26T03:17:33.067

7 Is the support of a flat sheaf flat? 2012-02-10T20:30:22.383

7 Triviality of direct multiples of flat complex vector bundles 2012-02-23T08:49:00.230

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

6 Torsion-free tensor powers 2011-08-18T03:28:14.833

6 Exactness of an additive left Kan extension 2014-11-24T17:47:55.897

6 Failure of universal flatification 2015-12-01T14:41:53.600

6 Lifting flat modules over ring quotients 2018-01-03T09:16:01.903

5 Under what hypotheses are schematic fixed points of a flat deformation themselves flat? 2010-10-24T22:06:52.517

5 When can a finite map be blown up to a flat one? 2011-08-03T18:09:01.163

5 Quotient of flat module is flat - a property in Mumford's Red book 2011-10-05T15:22:44.320

5 sections of morphisms of complex spaces 2011-11-16T01:01:00.800

5 Simultaneous resolution of singularities in special cases of flat families of projective varieties 2014-05-18T20:18:10.653

5 Injective flat module 2014-06-10T18:24:52.443

5 Tori in Compact Riemannian Symmetric Spaces 2014-09-21T01:03:17.140

5 Covering of schemes and flatness 2015-03-13T13:37:09.060

5 When is the flatness locus non-empty 2015-10-21T19:17:53.983

5 Descent of flatness from algebras to monoids 2016-10-31T13:28:13.880

5 Coherent subsheaf of co-admissible modules of Schneider and Teitelbaum 2017-02-08T16:08:07.703

4 The inverse limit of locally free module 2009-12-12T17:20:16.283

4 Rank 2 flat bundles on an elliptic curve, via extensions 2011-08-21T03:37:13.180

4 can one define the pullback between stacks of coherent sheaves for non-flat morphisms? 2011-09-01T10:32:40.630

4 Spreading out flat morphisms of schemes 2012-02-26T16:48:12.810

4 Are irreducible components of a flat family flat? 2012-11-22T13:50:29.943

4 Injectivity criterion for surjective coalgebra maps: does it hold in full generality? 2013-08-25T10:01:57.533

4 Faithful-flatness for maps of formal power series rings 2013-10-15T09:43:35.080

4 Extend a vector bundle on a flat family 2015-11-16T19:33:28.567

4 Being Cohen-Macaulay open in Hilbert scheme? 2016-08-02T18:21:28.673

3 Flatness of a homogeneous quasi-coherent sheaf on the formal plane from flatness on lines through the origin? 2010-12-16T08:28:12.207

3 Alternative module-theoretic characterization of flatness 2011-11-04T10:04:38.647

3 Subtle examples of morphisms that are finite but not flat 2012-01-14T20:13:44.227

3 Flatness for family of hypersurfaces 2012-05-10T22:08:22.017

3 is intersection of a curve and a family of curves generically constant as a scheme? 2012-06-24T13:54:09.660

3 On the m-th power of the Hodge bundle and Arakelov's theorem 2012-12-21T21:48:35.510

3 Formal criterion of flatness 2013-01-30T00:19:16.420

3 Affine hulls and base change 2014-08-26T20:30:09.167

3 Linear projection from a point and local complete intersection 2015-04-03T16:36:12.780

3 Which base change preserves integrality of schemes 2015-04-24T14:02:11.837

3 When is the pullback of an injective sheaf injective? 2016-08-04T05:58:32.227

3 Flatness of $Hom_R(M,M)$ 2017-02-24T18:52:06.920

2 Commutator tensors and submodules 2011-05-21T20:32:34.800

2 Flatness of sheaf of relative Kahler differentials 2011-09-14T15:11:02.130

2 Flatness over non-reduced schemes : no geometric characterisation 2011-10-23T13:58:22.017

2 properties of the fibers of a flat morphism 2012-04-26T17:11:29.583

2 Existence of the universal family for the Hilbert scheme of plane curves 2012-06-28T15:08:16.620

2 Are quotients of stacks flat? 2012-09-19T08:39:53.090

2 flatness criterion on normal bases 2012-12-22T19:06:40.223

2 Morphism with non-reduced special fibre 2013-04-21T19:14:09.567

2 flat and finite type morphisms 2013-06-23T14:57:00.943

2 on smoothness of morphisms on an artinian base 2013-09-01T13:45:02.160

2 morphism flat and relations 2013-12-11T21:49:29.417

2 Does the going-up theorem hold between flat algebras? 2014-03-06T15:07:33.203

2 $\delta$-functor and commutativity of pull-back with right derivation 2014-07-30T11:57:23.510

2 Ultraproducts and subobjects of projectives 2015-07-21T05:46:03.593

2 Deciding whether a non-f.g. non-divisible flat module is projective or not 2015-08-16T23:22:42.303

2 Projective dimension of a quotient ring 2015-08-31T14:21:44.340

2 Control of a meromorphic function according to distance between its zeros 2015-11-06T15:22:06.283

2 Are "vector spaces" over a smooth scheme with constant fiber dimension locally free? 2015-12-05T12:00:28.790

2 Is flatness preserved under exterior power 2016-03-05T09:54:59.450

2 Exterior power of a torsion-free sheaf on a DVR 2016-03-05T10:29:54.260

2 Torsion free sheaves in flat families 2016-03-23T20:46:52.500

2 Is the zero locus of a global section flat? 2016-06-04T04:09:29.927

2 Do finite flat sheaves define families of $0$-cycles? 2016-07-11T11:56:01.543

2 Descent of flatness from algebras to monoids II 2016-11-06T12:54:12.827

1 Flatness on the formal plane from flatness on lines through the origin? 2010-12-16T07:46:49.480

1 Projectivity and faithfully flatness (module theory) 2011-08-06T15:22:27.487

1 Cuspidal stable curves 2011-12-14T07:14:35.607

1 Relative generic flatness. 2012-02-09T15:57:36.983

1 1st-flat cohomology group for elliptic curves 2012-08-25T17:20:22.683

1 Does flatness/smoothness over special fiber imply flatness/smoothness globally? 2013-11-22T01:26:09.783

1 R[[X]] flat as a R[X]-module? 2014-07-05T14:59:00.203

1 Connectedness of fibers for flat, proper morphism 2015-03-25T12:33:15.020

1 Flatness and intersection of fibers 2015-03-31T13:01:45.630

1 quantum deformation 2015-05-10T13:47:29.680

1 Sections of proper, flat morphism 2015-06-24T16:33:14.057

1 A naive question on rational equivalence of varieties 2015-11-09T11:29:57.587

1 On simultaneous resolution of singularities in certain flat families 2016-08-13T16:33:58.883

1 Deformation of projective bundles 2017-04-29T22:38:55.540

0 The locus where a sheaf is supported in a certain dimension 2013-02-24T19:53:46.837