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...

Lyme disease is a persistent low-density spirochetosis caused by Borrelia burgdorferi sensu lato. Although spirochetes causing Lyme disease are highly immunogenic in experimental models, the onset of specific antibody responses to infection is often delayed or undetectable in some patients. The properties and mechanisms mediating such immune avoidance remain obscure. To examine the nature and c...

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...

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...

1. January 21, 2010 2 1.1. Why define a curve to be f rather than V (f) ⊂ P(k)? 3 1.2. Cubic plane curves 3 2. January 26, 2010 4 2.1. A little bit about smoothness 4 2.2. Weierstrass form 5 3. January 28, 2010 6 3.1. An algebro-geometric description of the group law in terms of divisors 6 3.2. Why are the two group laws the same? 7 4. February 2, 2010 7 4.1. Overview 7 4.2. Uniqueness of Weier...

τ(n)e(nz). The two equations were proven for τ(n) by Mordell, using what are now known as the Hecke operators. The inequality was proven by Deligne as a consequence of his proof of the Weil conjectures. Those results determine everything about af (n) except for the distribution of the af (p) ∈ [−2, 2]. Define θf (p) ∈ [0, π] by af (p) = 2 cos θf (p). It is conjectured that for each f the θf (p)...

In this article we develop a broad generalization of the classical Bost-Connes system, where roots of unit are replaced by an algebraic datum consisting of an abelian group and a semi-group of endomorphisms. Examples include roots of unit, Weil restriction, algebraic numbers, Weil numbers, CM fields, germs, completion of Weil numbers, etc. Making use of the Tannakian formalism, we categorify th...

In this talk the definition of polarization of abelian variety and Weil paring will be given. After introducing some proposition of Weil pairing, we will show the Zarhin’s trick about principal polarization.

We describe how to prove the Mordell-Weil theorem for Jacobians of hyperelliptic curves over Q and how to compute the rank and generators for the Mordell-Weil group.