Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

The kommuna impulse: collective mechanisms and commune-ists in the early Soviet State

This study examines the creation of the urban kommuna (commune) and the ideals that stimulated this social phenomenon – the kommuna impulse of the nascent Soviet state. Collective idealism affected Soviet housing, architecture and even urban planning, but little is known of social experiments in commune‐ism. As a result, these collective cells have been dismissed as utopian anomalies or the product of a housing shortage. Here it is argued that these discursive assessments are unsatisfactory and isolated from the historical narrative. While utopian ideals and domestic necessity were central to the formation of collective living, the kommuna was also involved in an active discourse with collectivism and socialist ideology. The kommuna cell was a dynamic entity that required considerable formative planning. The activists who forged these cells – the self‐identified ‘communards’ – turned their everyday domestic life into a socialist battleground, in which they struggled with the key debates of the early Soviet state. This article examines the communard as a social activist in order to better understand this phenomenon. It clarifies the coexistence of ideological and idealist trends among Soviet youth with practical contingencies for socialism. Furthermore, it reveals the process by which the kommuna impulse and these contingencies developed throughout the 1920s and early 1930s.

The rise and fall of Benedetto Croce: intellectual positionings in the Italian cultural field 1944-1947

This article evaluates the discourse developed around Benedetto Croce in the Italian cultural periodical press between 1944 and 1947 and it discusses the forms of adversarial discourse and the agents involved in the anti-Croce polemics that unfolded in the Communist party’s official cultural journal Rinascita. Specifically, this article focuses on a selection of intellectuals who moved away from Crocean idealism to embrace Marxism in order to investigate how their conversion was presented in Rinascita.