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Multiplicative maps from Hℤ to a ring spectrum R-a naive version

Stanisław Betley (2012)

Fundamenta Mathematicae

The paper is devoted to the study of the space of multiplicative maps from the Eilenberg-MacLane spectrum Hℤ to an arbitrary ring spectrum R. We try to generalize the approach of Schwede [Geom. Topol. 8 (2004)], where the case of a very special R was studied. In particular we propose a definition of a formal group law in any ring spectrum, which might be of independent interest.

Normality and non-normality of group compactifications in simple projective spaces

Paolo Bravi, Jacopo Gandini, Andrea Maffei, Alessandro Ruzzi (2011)

Annales de l’institut Fourier

Given an irreducible representation V of a complex simply connected semisimple algebraic group G we consider the closure X of the image of G in ( End ( V ) ) . We determine for which V the variety X is normal and for which V is smooth.

On a conjecture of Kottwitz and Rapoport

Qëndrim R. Gashi (2010)

Annales scientifiques de l'École Normale Supérieure

We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all (connected) split and quasi-split unramified reductive groups. Our results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.

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