In this article, following an insight of Kontsevich, we extend the Weil conjecture, as well strong form Tate from realm algebraic geometry to broad noncommutative setting dg categories. Moreover, establish a functional equation for Hasse-Weil zeta functions, compute l-adic and p-adic absolute values eigenvalues cyclotomic Frobenius, provide complete description category numerical motives in ter...

We give a construction of Connes-Moscovici’s cyclic cohomology for any Hopf algebra equipped with a character. Furthermore, we introduce a non-commutative Weil complex, which connects the work of Gelfand and Smirnov with cyclic cohomology. We show how the Weil complex arises naturally when looking at Hopf algebra actions and invariant higher traces, to give a non-commutative version of the usua...

Let Sg be a closed surface of genus g and Mg be the moduli space of Sg endowed with the Weil-Petersson metric. In this paper we investigate the Weil-Petersson curvatures of Mg for large genus g. First, we study the asymptotic behavior of the extremal Weil-Petersson holomorphic sectional curvatures at certain thick surfaces in Mg as g → ∞. Then we prove two curvature properties on the whole spac...

We use ending laminations for Weil-Petersson geodesics to establish that bounded geometry is equivalent to bounded combinatorics for WeilPetersson geodesic segments, rays, and lines. Further, a more general notion of non-annular bounded combinatorics, which allows arbitrarily large Dehn-twisting, corresponds to an equivalent condition for Weil-Petersson geodesics. As an application, we show the...

Abstract. A parity checking-styled Weil sum algorithm is presented for a general class of the univariate polynomials which fully characterize a system of n polynomials in n variables over F2. The previously known proof methods of explicit Weil sum evaluation of Dembowski-Ostrom polynomials are extended to general case. The algorithm computes the absolute values of the Weil sums of the generic c...

With contributions from: Maarten Menken, Heiner Stuckenschmidt, Holger Wache (Vrije Universiteit Amsterdam) Luciano Serafini (Centro per la Ricerca Scientifica e Tecnologica, Trento) Andrei Tamilin (Università degli Studi di Trento) Mustafa Jarrar (Vrije Universiteit Brussel) Fabio Porto (Ecole Polytechnique Fédérale de Lausanne) Christine Parent (Université de Lausanne) Alan Rector, Jeff Pan (...

The World Health Organization/Food and Agricultural Organization Collaborating Centre for Reference and Research on Leptospirosis, Western Pacific Region, accredited since 1958, is part of Queensland Health Scientific Services, which provide tertiary level support in epidemiology, surveillance, training and diagnosis for hospitals and pathology laboratories across the State. Databases for lepto...

We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections. The main purpose of the present paper is to describe some geometric properties of the category FMm of fibered manifolds with m-dimensional bases and local fib...