We derive an étale descent formula for topological Hochschild homology and prove a HKR theorem for smooth S-algebras.

The analogue of Goldie's Theorem for prime rings is proved for rings graded by abelian groups, eliminating unnecessary additional hypotheses used in earlier versions.

The-calculus is an extension of the-calculus that has been introduced by M Parigot to give an algorithmic content to classical proofs. We show that B ¨ ohm's theorem fails in this calculus. §1. Introduction. The-calculus (its typed and untyped versions) has been introduced by M. Parigot in [6]. Its typed version is an extension of the typed-calculus intended to give an algorithmic content to cl...

In this work we generalize the celebrated Rees’s theorem for arbitrary ideals in a local ring by using the Achilles-Manaresi multiplicity sequence as a generalization of the Hilbert-Samuel multiplicity.

A variety of inaccurate claims about Gold's Theorem have appeared in the cognitive science literature. I begin by characterizing the logic of this theorem and its proof. I then examine several claims about Gold's Theorem, and I show why they are false. Finally, I assess the significance of Gold's Theorem for cognitive science. 1. Introduction. Over the years, negative evidence in language acqui...

Let lu = −u + q(x)u, where q(x) is a real-valued L 2 loc (0, ∞) function. H. Weyl has proved in 1910 that for any z, Imz = 0, the equation (l − z)w = 0, x > 0, has a solution w ∈ L 2 (0, ∞). We prove this classical result using a new argument.

Bell’s theorem depends crucially on counterfactual reasoning, and is mistakenly interpreted as ruling out a local explanation for the correlations which can be observed between the results of measurements performed on spatially-separated quantum systems. But in fact the Everett interpretation of quantum mechanics, in the Heisenberg picture, provides an alternative local explanation for such cor...

numbers. As applications we obtain a new formula for the Fibonacci quotient Fp−( 5 p )/p and a criterion for the relation p |F(p−1)/4 (if p ≡ 1 (mod 4)), where p 6= 5 is an odd prime. We also prove that the affirmative answer to Wall’s question implies the first case of FLT (Fermat’s last theorem); from this it follows that the first case of FLT holds for those exponents which are (odd) Fibonac...

Let X be a smooth curve over a finite field of characteristic p , let l 6= p be a prime number, and let L be an irreducible lisse Ql -sheaf on X whose determinant is of finite order. By a theorem of L. Lafforgue, for each prime number l 6= p , there exists an irreducible lisse Ql′ -sheaf L ′ on X which is compatible with L , in the sense that at every closed point x of X , the characteristic po...

Let A be the polynomial ring over k (a field of characteristic zero) in n + 1 variables. The commuting derivations conjecture states that n commuting locally nilpotent derivations on A, linearly independent over A, must satisfy A D 1 ,...,Dm = k[f ] where f is a coordinate. The conjecture can be formulated as stating that a (G m) n-action on k n+1 must have invariant ring k[f ] where f is a coo...