We initiate the study of Nash blowups in prime characteristic. First, we show that a normal variety is non-singular if and only its blowup an isomorphism, extending theorem by A. Nobile. also higher blowups, as defined T. Yasuda. Specifically, give characteristic-free proof version Nobile’s for quotient varieties hypersurfaces. prove weaker $F$-pure varieties.

The sub algebra functor Sub A is faithful for Boolean algebras (Sub A •Sub B implies A • B, see D. Sachs [7] ), but it is not faithful for bounded distributive lattices or unbounded distributive lattices. The automorphism functor Aut A is highly unfaithful even for Boolean algebras. The endomorphism functor End A is the most faithful of all three. B. M. Schein [8] and K. D.' Magill [5] establis...

Now we proceed to study representations of quivers. We start by recalling some basic definitions and constructions such as the path algebra and indecomposable representations. Then we state a theorem of Kac that describes the dimensions, where the indecomposable representations occur as well as the number of parameters needed to describe their isomorphism classes. We will prove the Kac theorem ...

We present a general method for constructing families of measure preserving transformations which are K and loosely Bernoulli with various ergodic theoretical properties. For example, we construct two K transformations which are weakly isomorphic but not isomorphic, and a K transformation with no roots. Ornstein’s isomorphism theorem says families of Bernoulli shifts cannot have these propertie...

The purpose of this note is to state a collection of results, all related to questions of uniqueness of smooth neighborhoods of finite complexes as imbedded (nicely) in differentiable manifolds. The reported results will appear in subsequent papers, the first of which is [l ]. The approach taken is always via the theory of simple homotopy types (due to J. H. C. Whitehead), and the main theorem ...

Landau-Ginzburg mirror symmetry studies isomorphisms between Aand B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial W and a related symmetry group G. Given two polynomials W1, W2 with the same weights and same group G, the corresponding A-models built with (W1,G) and (W2,G) are isomorphic. Though the same result cannot hold in full genera...

Classification theory guarantees the existence of an isomorphism between any two E8’s, at least over an algebraically closed field of characteristic 0. The purpose of this paper is to construct for any Jordan algebra J of degree 3 over a field Φ of characteristic ≠ 2,3 an explicit isomorphism between the algebra obtained from J by Faulkner’s construction and the algebra obtained from the split ...

We show in §1 that the Ax-Kochen isomorphism theorem [AK] requires the continuum hypothesis. Most of the applications of this theorem are insensitive to set theoretic considerations. (A probable exception is the work of Moloney [Mo].) In §2 we give an unrelated result on cuts in models of Peano arithmetic which answers a question on the ideal structure of countable ultraproducts of Z posed in [...

The goal of this paper is to prove the equivariant version of Bloch’s Riemann-Roch isomorphism between the higher algebraic K-theory and the higher Chow groups of smooth varieties. We show that for a linear algebraic group G acting on a smooth variety X , although there is no Chern character map from the equivariant K-groups to equivariant higher Chow groups, there is indeed such a map K i (X)⊗...

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out a sequence of examples. We follow recent work by...