On Harder-Narasimhan filtrations and their compatibility with tensor products

We attach buildings to modular lattices and use them to develop a metric approach to Harder-Narasimhan filtrations. Switching back to a categorical framework, we establish an abstract numerical criterion for the compatibility of these filtrations with tensor products. We finally verify our criterion in three cases, one of which is new

Mazur's inequality and laffaille's theorem

We look at various questions related to filtrations in $p$-adic Hodgetheory, using a blend of building and Tannakian tools. Specifically,Fontaine and Rapoport used a theorem of Laffaille on filtered isocrystalsto establish a converse of Mazur's inequality for isocrystals. Wegeneralize both results to the setting of (filtered) $G$-isocrystalsand also establish an analog of Totaro's $\otimes$-product theoremfor the Harder-Narasimhan filtration of Fargues

Liftings of Reduction Maps for Quaternion Algebras

We construct liftings of reduction maps from CM points to supersingular points for general quaternion algebras and use these liftings to establish a precise correspondence between CM points on indefinite quaternion algebras with a given conductor and CM points on certain corresponding totally definite quaternion algebras.Comment: 17 page

Mary Wollstonecraft's A vindication of the rights of women as generator of differing feminist traditions

Although the name of Mary Wollstonecraft still stands high in the annals of feminism as one of the earliest promoters of the feminist ideal of human equal rights, a closer look at the development of feminism along the nineteenth century reveals that A Vlndication of the Rights of Women did not influence solely the movement for the emancipation of women or Equal Rights Movement (too often presented as the only existing type of feminism at the time). Some of the ideas advanced by the author in her famous book were likewise appropriated by another type of feminism which upheld women's DIFFERENCE from man rather than their similarity. The purpose of this article is therefore to analyze how and why Mary Wollstonecraft's A Vlndication of the Rights of Women can be considered as having given rise to two different and indeed, sometimes contradictory approaches to feminism