Let A be a finitely generated algebra over a field K of characteristic p > 0. We introduce a subring W †(A) ⊂ W (A), which we call the ring of overconvergent Witt vectors and prove its basic properties. In a subsequent paper we use the results to define an overconvergent de Rham-Witt complex for smooth varieties over K whose hypercohomology is the rigid cohomology.

Let X be an algebraic variety over the field of real numbers R. We use the signature of a quadratic form to produce “higher” global signatures relating the derived Witt groups of X to the singular cohomology of the real points X(R) with integer coefficients. We also study the global signature ring homomorphism and use the powers of the fundamental ideal in the Witt ring to prove an integral ver...

Given a formal power series f(z) ∈ C[[z]] we define, for any positive integer r, its rth Witt transform, W (r) f , by W (r) f (z) = 1 r ∑ d|r μ(d)f(z d)r/d, where μ denotes the Möbius function. The Witt transform generalizes the necklace polynomials, M(α;n), that occur in the cyclotomic identity 1 1− αy = ∞

We write the Hamiltonain for a gravitational spherically symmetric scalar field collapse with massive scalar field source, and we discuss the application of Wheeler De Witt equation as well as the appearence of time in this context. Using an Ansatz for Wheeler De Witt equation, solutions are discussed including the appearence of time evolution. [email protected]/[email protected] khanna@phys....

(A) All rings in this announcement are commutative and with 1. For any ring K we denote by W(K) the Witt ring of nondegenerate symmetric bilinear forms over K. DEFINITION 1. A signature o of K is a ring homomorphism from W(K) to Z. REMARK 1. If K is a field, the signatures correspond uniquely with the orderings of K [3], [9]. Thus Theorem 1 below generalizes the main results of Artin-Schreier's...

We compute the total Witt groups of (split) Grassmann varieties, over any regular base X. The answer is a free module over the total Witt ring of X. We provide an explicit basis for this free module, which is indexed by a special class of Young diagrams, that we call even Young diagrams.

Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. In this paper, we investigate some properties of Boole polynomials and consider Witt-type formulas for the Boole numbers and polynomials. Finally, we derive some new identities of those poly-nomials from the Witt-type formulas which are related to Euler polynomials.