37 citations · 188 across the 35 of their papers we have counts for
42 papers
The topology of Kähler manifolds and 1-forms without zeros
Maurício Corrêa, János Kollár, Stefan Schreieder +1
We study how the topology and geometry of a compact Kähler manifold relate to the zeros of its one-forms. We determine all implications among several closely related conditions. In…
Two proofs of the Cassels--Swinnerton-Dyer conjecture for cubic surfaces
Valery Alexeev, Stefan Schreieder
The Cassels--Swinnerton-Dyer conjecture asserts that a cubic hypersurface contains a rational point if and only if it contains a point of degree coprime to , or, equivalently, a…
Zeros of one-forms and the topology of algebraic maps
Stefan Schreieder, Botong Wang
We construct a smooth complex projective variety whose Albanese morphism is a homotopy fiber bundle but not a submersion. The same variety fibers smoothly over the circle, although…
Invisible singularities in complex algebraic geometry
Maurício Corrêa, János Kollár, Stefan Schreieder +1
We construct morphisms between smooth complex projective varieties that have singular fibers, but look topologically smooth. We use this to give negative answers to the following f…
Matroids and the integral Hodge conjecture for abelian varieties
Philip Engel, Olivier de Gaay Fortman, Stefan Schreieder
We prove that the cohomology class of any curve on a very general principally polarized abelian variety of dimension at least 4 is an even multiple of the minimal class. The same h…
Combinatorics and Hodge theory of degenerations of abelian varieties: A survey of the Mumford construction
Philip Engel, Olivier de Gaay Fortman, Stefan Schreieder
We survey the Mumford construction of degenerating abelian varieties, with a focus on the analytic version of the construction, and its relation to toric geometry. Moreover, we stu…
On the rationality problem for low degree hypersurfaces
Jan Lange, Stefan Schreieder
We show that a very general hypersurface of degree d at least 4 and dimension at most over a field of characteristic different from 2 does not admit a decomposition…
Remarks on Milnor K-theory and Tate's conjecture for divisors
Stefan Schreieder
We show that the Tate conjecture for divisors over a finite field is equivalent to an explicit algebraic problem about the third Milnor K-group of the function field $\…
Cycle conjectures and birational invariants over finite fields
Samet Balkan, Stefan Schreieder
We study a natural birational invariant for varieties over finite fields and show that its vanishing on projective space is equivalent to the Tate conjecture, the Beilinson conject…
Truncated pushforwards and refined unramified cohomology
Theodosis Alexandrou, Stefan Schreieder
For a large class of cohomology theories, we prove that refined unramified cohomology is canonically isomorphic to the hypercohomology of a natural truncated complex of Zariski she…
Abelian varieties with no power isogenous to a Jacobian
Olivier de Gaay Fortman, Stefan Schreieder
For a curve of genus at least four which is either very general or very general hyperelliptic, we classify all ways in which a power of its Jacobian can be isogenous to a product o…
Geometric retract rationality of norm varieties
Stefan Schreieder
Let k be a field of characteristic zero. We show that the norm variety associated to a prime and an ordered sequence of invertible elements of k is geometrically retract rat…
Zeros of one-forms and homologically trivial fibrations
Stefan Schreieder, Ruijie Yang
We show that a conjecture of Kotschick about one-forms without zeros on compact Kähler manifolds follows in the case of simple Albanese torus from a conjecture of Bobadilla and Kol…
On Bloch's map for torsion cycles over non-closed fields
Theodosis Alexandrou, Stefan Schreieder
We generalize Bloch's map on torsion cycles from algebraically closed fields to arbitrary fields. While Bloch's map over algebraically closed fields is injective for zero-cycles an…
A moving lemma for cohomology with support
Stefan Schreieder
For a natural class of cohomology theories with support (including étale or pro-étale cohomology with suitable coefficients), we prove a moving lemma for cohomology classes with su…
Unramified cohomology, algebraic cycles and rationality
Stefan Schreieder
This is a survey on unramified cohomology with a view towards its applications to rationality problems.
The diagonal of quartic fivefolds
Nebojsa Pavic, Stefan Schreieder
We show that a very general quartic hypersurface in over a field of characteristic different from 2 does not admit a decomposition of the diagonal, hence is not retr…
Infinite torsion in Griffiths groups
Stefan Schreieder
We show that there are smooth complex projective varieties with infinite 2-torsion in their third Griffiths groups. It follows that the torsion subgroup of Griffiths groups is in g…
Refined unramified cohomology of schemes
Stefan Schreieder
We introduce the notion of refined unramified cohomology of algebraic schemes and prove comparison theorems that identify some of these groups with cycle groups. This recovers for…
Equality in the Bogomolov--Miyaoka--Yau inequality in the non-general type case
Feng Hao, Stefan Schreieder
We classify all minimal models X of dimension n, Kodaira dimension n-1 and with vanishing Chern number . This solves a problem of Kollár. Completing previous wor…
Torsion orders of Fano hypersurfaces
Stefan Schreieder
We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametr…
Chern numbers of uniruled threefolds
Stefan Schreieder, Luca Tasin
In this paper we show that the Chern numbers of a smooth Mori fibre space in dimension three are bounded in terms of the underlying topological manifold. We also generalise a theor…
Holomorphic one-forms without zeros on threefolds
Feng Hao, Stefan Schreieder
We show that a smooth complex projective threefold admits a holomorphic one-form without zeros if and only if the underlying real 6-manifold fibres smoothly over the circle, and we…
Zeros of holomorphic one-forms and topology of Kähler manifolds
Stefan Schreieder
A conjecture of Kotschick predicts that a compact Kähler manifold fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper w…