Jean-Louis Colliot-Thélène Alexei N. Skorobogatov Page 1 The Brauer– Grothendieck Group
Jean-Louis Colliot-Thélène Alexei N. Skorobogatov Ergebnisse der Mathematik und ihrer …

We consider the problem of counting the number of varieties in a family over a number field
which contain a rational point. In particular, for products of Brauer–Severi varieties and …

We study the distribution of extensions of a number field k with fixed abelian Galois group G,
from which a given finite set of elements of k are norms. In particular, we show the existence …

An upper bound sieve for rational points on suitable varieties is developed, together with
applications to counting rational points in thin sets, to local solubility in families, and to the …

In this paper we investigate the quantity of diagonal quartic surfaces which have a Brauer–
Manin obstruction to the Hasse principle. We are able to find an asymptotic formula for the …

We consider the problem of counting the number of varieties in a family over Q with a
rational point. We obtain lower bounds for this counting problem for some families over P1 …

Rational points on Del Pezzo surfaces of degree four Page 1 International Journal of Number
Theory Vol. 18, No. 9 (2022) 2099–2127 © World Scientific Publishing Company DOI …

A less known event of 1968 in Paris was the publication of “Dix exposés sur la cohomologie
des schémas” by J. Giraud, A. Grothendieck, SL Kleiman, M. Raynaud and J. Tate. Included …

Let $ f: X\to Y $ be a dominant morphism of smooth, proper and geometrically integral
varieties over a number field $ k $, with geometrically integral generic fibre. We give a …

Abstract We resolve Schinzel's Hypothesis (H) for 100% of polynomials of arbitrary degrees.
We deduce that a positive proportion of diagonal conic bundles over Q with any given …