It is shown that the obvious method of descending from an element of the 2-Selmer group of an elliptic curve, E, will indeed give elements of order 1, 2 or 4 in the Weil-Chatelet group of E. Explicit algorithms for such a method are given.

of the Dissertation On some computational and analytic aspects of Chern-Weil forms

The Weil pairing of two element from the torsion of the Jacobian of an algebraic curve may be given by a product of local Hilbert symbols of two special idèles associated to the torsion elements of the Jacobian. On the other hand Arbarello, de Concini and Kac have constructed some central extension of the group of idèles on an algebraic curve, in which the commutator is also equal up to sign to...

In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses we can find m...

This paper contains two main results. The first is the existence of an equivariant Weil-Petersson geodesic in Teichmüller space for any choice of pseudo-Anosov mapping class. As a consequence one obtains a classification of the elements of the mapping class group as WeilPetersson isometries which is parallel to the Thurston classification. The second result concerns the asymptotic behavior of t...

In this note we announce an extension of these theorems to the setting of Stiefel manifolds and matrix space. Our work makes it possible to construct holomorphic discrete series representations for the real symplectic group by decomposing a tensor product of certain projective representations introduced earlier by Shale and Weil. (See Weil [11] and also Shalika [10].) Proofs of the results anno...

In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses we can find m...

BACKGROUND AND OBJECTIVE Rickettsial infections are an important cause of undifferentiated febrile illness in tropics. While scrub typhus was reported from Goa, other rickettsial infections have not been reported earlier. The present study was planned to identify pattern of rickettsial infections in Goa. MATERIALS AND METHODS All patients presenting with undiagnosed acute febrile illness were...

BACKGROUND & OBJECTIVES Rickettsial infections remain under-diagnosed due to lack of diagnostic facilities in developing world. Here we present our experience at National Centre for Disease Control, Delhi, about a serosurvey done in Delhi for rickettsial disease with easy to perform low cost, low expertise Weil Felix test. METHODS On the basis of cut-off titre obtained in healthy population, ...