The starting point of this method is Falting’s article in which he proves the Mordell-Weil theorem. He remarked and Serre turned it into a working method, the fact that the equivalence of two λ-adic representations is something that can be basically determined on some finite extension of the base field (even though the representations might not factor through a finite quotient). Let Oλ be the r...

Using a multidimensional large sieve inequality, we obtain a bound for the mean square error in the Chebotarev theorem for division fields of elliptic curves that is as strong as what is implied by the Generalized Riemann Hypothesis. As an application we prove a theorem to the effect that, according to height, almost all elliptic curves are Serre curves, where a Serre curve is an elliptic curve...

Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result under certain mild restrictions on the level and character to the case of weight 1/2 Hilbert modular forms over a totally real field of narrow class number 1. The methods broadly follow those of Serre-Stark; however we are forced to overcome technical di...

1. Exact couples and spectral sequences 2 1.1. Spectral sequences 2 1.2. Exact couples 2 1.3. The spectral sequence associated to an exact couple 3 1.4. Example: the spectral sequence of a filtered space 3 References 4 2. Pages of the spectral sequence 4 2.1. Iterated subquotients 4 2.2. Formula for the rth page 5 2.3. Filtered spaces 6 3. Convergence 6 3.1. Simplest case: first quadrant spectr...

A preliminary set of experiments are described in which a biologically-inspired computer vision system (Serre, Wolf et al. 2005; Serre 2006; Serre, Oliva et al. 2006; Serre, Wolf et al. 2006) designed for visual object recognition was applied to the task of phonetic classification. During learning, the system processed 2-D wideband magnitude spectrograms directly as images, producing a set of 2...

the blow-up of |KC +D| along the image of C (which we will also denote by C). In contrast, the Serre correspondence is a morphism only when d ≤ 2, as it is undefined at points of C (and certain secant varieties) for larger values of d. The structure of the Serre correspondence for large d (particularly d > 2g − 2, in which case it is dominant) is, however, well understood now, due largely to re...

We exhibit Cartwright-Curien-Felleisen’s model of observably sequential algorithms as a full subcategory of Laird’s bistable biorders, thereby reconciling two views of functions: functions-as-algorithms (or programs), and functions-as-relations. We then characterize affine sequential algorithms as affine bistable functions in the full subcategory of locally boolean orders.