Related papers: All subterminal schemes
It is known that the spin structure on a Riemannian manifold can be extended to noncommutative geometry using the notion of a spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
We study the property of a normal scheme, that the complement of every hypersurface is an affine scheme. To this end we introduce the affine class group. It is a factor group of the divisor class group and measures the deviation from this…
We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine…
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…
We introduce perfect resolving algebras and study their fundamental properties. These algebras are basic for our theory of differential graded schemes, as they give rise to affine differential graded schemes. We also introduce etale…
We define a partition of a reductive group into finitely many subsets, refining the partition of the group into strata. We state some conjectural properties of these subsets (called substrata) and verify them in some examples.
We prove that finite sets of mutual neighbor points in an affine scheme admit affine combinations, preserved by any map. Furthermore, such combination has a value which is neighbor point of all the original points.
The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…
Every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andre-Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A-infinity ring spectra and for…
We extend the definition of fundamental group scheme to non reduced schemes over any connected Dedekind scheme. Then we compare the fundamental group scheme of an affine scheme with that of its reduced part.
We prove that if a group scheme of multiplicative type acts on an algebraic stack with affine, finitely presented diagonal then the stack of fixed points is algebraic. For this, we extend two theorems of [SGA3.2] on functors of subgroups of…
In this paper we aim to characterize association schemes all of whose symmetric fusion schemes have only integral eigenvalues, and classify those obtained from a regular action of a finite group by taking its orbitals.
We classify surjective self-maps (of degree at least two) of affine surfaces according to the log Kodaira dimension.
The spectral projectors method is a way to obtain a theoretically well posed definition of the topological susceptibility on the lattice. Up to now this method has been defined and applied only to Wilson fermions. The goal of this work is…
We construct a 2-category of differential graded schemes. The local affine models in this theory are differential graded algebras, which are graded commutative with unit over a field of characteristic zero, are concentrated in non-positive…
We develop a sequential-topological study of rational points of schemes of finite type over local rings typical in higher dimensional number theory and algebraic geometry. These rings are certain types of multidimensional complete fields…
In this note, finite type epimorphisms of rings are characterized.
We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite composition series whose factors are either reductive or proper, flat, finitely presented, acting on algebraic stacks with affine,…
We discuss the classification of reflection subgroups of finite and affine Weyl groups from the point of view of their root systems. A short case free proof is given of the well known classification of the isomorphism classes of reflection…