The Euler characteristic of varieties realized as the complete intersection of toric hypersurfaces.
The Euler series of restricted Chow varieties
The existence of higher logarithms
The explicit reciprocity law and the cohomology of Fontaine-Messing
The Formal Hodge Filtration.
The fundamental group at infinity of affine surfaces.
The fundamental group of a Galois cover of .
The fundamental group of a locally finite graph with ends-a hyperfinite approach
The end compactification |Γ| of a locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π₁(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also show how to recover the standard description of π₁(|Γ|) given by Diestel and Sprüssel (2011). Finally, we give...
The Fundamental Group of the Complement of a Union of Complex Hyperplanes.
The fundamental group of the complement of a union of complex hyperplanes: correction.
The Fundamental Group of the Complement of an Algebraic Curve.
The fundamental groupoid scheme and applications
We define a linear structure on Grothendieck’s arithmetic fundamental group of a scheme defined over a field of characteristic 0. It allows us to link the existence of sections of the Galois group to with the existence of a neutral fiber functor on the category which linearizes it. We apply the construction to affine curves and neutral fiber functors coming from a tangent vector at a rational point at infinity, in order to follow this rational point in the universal covering of the affine...
The Fundamental Group-Scheme of an Abelian Variety.
The Galois structure of S-units
The Galois-module structure of the space of holomorphic differentials of a curve.
The Grothendieck group of G-equivariant modules over coordinate rings of G-orbits
The hard Lefschetz theorem and the topology of semismall maps
The Hilbert Modular Surface for the Ideal (...5) and the Horrocks-Mumford Bundle.
The Hilbert schemes of degree three curves
The Hodge Conjecture for a Certain Class of Fourfolds.