arXiv subjects
Publications and source records attributed to R. Sujatha.
Given a functor $T:C \to D$ carrying a class of morphisms $S\subset C$ into a class $S'\subset D$, we give sufficient conditions in order that $T$ induces an equivalence on the localised categories. These conditions are in the spirit of Quillen's theorem A. We give some applications in algebaic and birational geometry.
The main conjectures of Iwasawa theory provide the only general method known at present for studying the mysterious relationship between purely arithmetic problems and the special values of complex L-functions, typified by the conjecture of Birch and Swinnerton-Dyer and its generalizations. Our goal in the present paper is to develop algebraic techniques which enable us to formulate a precise version of such a main conjecture for motives over a large class of p-adic Lie extensions of number fields. The paper ends by formulating and briefly discussing the main conjecture for an elliptic curve E over the rationals Q over the field generated by the coordinates of its p-power division points, where p is a prime greater than 3 of good ordinary reduction for E.
A theorem of Grothendieck asserts that over a perfect field k of cohomological dimension one, all non-abelian H^2-cohomology sets of algebraic groups are trivial. The purpose of this paper is to establish a formally real generalization of this theorem. The generalization -- to the context of perfect fields of virtual cohomological dimension one -- takes the form of a local-global principle for the H^2-sets with respect to the orderings of the field. This principle asserts in particular that an element in H^2 is neutral precisely when it is neutral in the real closure with respect to every ordering in a dense subset of the real spectrum of k. Our techniques provide a new proof of Grothendieck's original theorem. An application to homogeneous spaces over k is also given.
Let Y be a real Enriques surface, _2Br(Y) the subgroup of elements of order 2 of Br(Y), and s, s_{or}, and s_{nor} the number of all connected, connected orientable, and connected non-orientable components of Y(R) respectively. Using universal covering K3-surface X of Y, we connect dim _2Br(Y) with the s, s_{or} and s_{nor}. As a geometric corollary of our considerations, we show that s \le 6 and s_{nor} \le 4.