Related papers: Rojtman's theorem for normal schemes

For smooth projective G-varieties, we equate the gauged Gromov-Witten invariants for sufficiently small area and genus zero with the invariant part of equivariant Gromov-Witten invariants. As an application we deduce a gauged version of…

We extend previous work on Hrushovski's stabilizer's theorem and prove a measure-theoretic version of a well-known result of Pillay-Scanlon-Wagner on products of three types. This generalizes results of Gowers on products of three sets and…

Let $X$ be a normal variety over a perfect field of positive characteristic and $B$ a reduced divisor on $X$. We prove that if the Cartier isomorphism on the log smooth locus of $(X,B)$ extends to the entire $X$, then $(X,B)$ satisfies the…

We provide a cohomological interpretation of the zeroth stable $\mathbb{A}^1$-homotopy group of a smooth curve over an infinite perfect field. We show that this group is isomorphic to the first Nisnevich (or Zariski) cohomology group of a…

The classical Bott-Samelson theorem states that if on a Riemannian manifold all geodesics issuing from a certain point return to this point, then the universal cover of the manifold has the cohomology ring of a compact rank one symmetric…

The Riemann-Roch Theorem is one of the cornerstones of algebraic geometry, connecting algebraic data (sheaf cohomology) with geometric ones (intersection theory). This survey paper provides a self-contained introduction and a complete proof…

In this paper we study the \'etale cohomology groups associated to abelian varieties. We obtain necessary and sufficient conditions for an abelian variety to have semistable reduction (or purely additive reduction which becomes semistable…

In this article, we introduce the notion of global adelic space of an arithmetic variety over an adelic curve and prove an equidistribution theorem for a generic sequence of subvarieties. As an application, we prove a Bogomolov type theorem…

We show that the zero locus of a normal function on a smooth complex algebraic variety S is algebraic provided that the normal function extends to a admissible normal function on a smooth compactification of S with torsion singularity. This…

Anabelian geometry with etale homotopy types generalizes in a natural way classical anabelian geometry with etale fundamental groups. We show that, both in the classical and the generalized sense, any point of a smooth variety over a field…

We prove a general version of the homological perturbation lemma which works in the presence of curvature, and without the restriction to strong deformation retracts, building on work of Markl. A key observation is that the notion of strong…

We discuss Iitaka's theory of quasi-Albanese maps in details. We also give a detailed proof of Kawamata's theorem on the quasi-Albanese maps for varieties of the logarithmic Kodaira dimension zero. Note that Iitaka's theory is an…

We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic p (as defined by Abramovich, Olsson, and Vistoli) which lift mod p^2 degenerates. We push the result to the coarse spaces of such…

Given a holomorphic selfmap f of the complex projective plane of algebraic degree at least 2, we give sufficient conditions on a positive closed (1,1) current S of unit mass under which the normalized pullbacks of S under iterates of f…

Suppose a residually finite group $G$ acts cocompactly on a contractible complex with strict fundamental domain $Q$, where the stabilizers are either trivial or have normal $\mathbb{Z}$-subgroups. Let $\partial Q$ be the subcomplex of $Q$…

In this note, we provide a description of the structure of homomorphisms from a finitely generated group to any torsion-free (3-dimensional) Kleinian group with uniformly bounded finite covolume. This is analogous to the Jorgensen-Thurston…

The classical Skolem--Noether Theorem [Giraud, 71] shows us (1) how we can assign to an Azumaya algebra $A$ on a scheme $X$ a cohomological Brauer class in $H^2(X,\mathbf G_m)$ and (2) how Azumaya algebras correspond to twisted vector…

In this expository article, we give a survey of Adrian Ioana's cocycle superrigidity theorem for profinite actions of Property (T) groups, and its applications to ergodic theory and set theory. In addition to a statement and proof of…

We explain how Johnstone's 1989 proof of the closed subgroup theorem for localic groups can be viewed as a point-free version of Pettis's theorem for Baire topological groups. We then use it to derive localic versions of the open mapping…

Let k be an algebraically closed subfield of the complex numbers, and X a variety defined over k. One version of the Beilinson-Hodge conjecture that seems to survive scrutiny is the statement that the Betti cycle class map cl_{r,m} :…