29 citations · 185 across the 37 of their papers we have counts for
5 papers · 2 filters
Blue schemes, semiring schemes, and relative schemes after Toën and Vaquié
Oliver Lorscheid
It is a classical insight that the Yoneda embedding defines an equivalence of schemes as locally ringed spaces with schemes as sheaves on the big Zariski site. Similarly, the Yoned…
On Schubert decompositions of quiver Grassmannians
Oliver Lorscheid
In this paper, we introduce Schubert decompositions for quiver Grassmannians and investigate example classes of quiver Grassmannians with a Schubert decomposition into affine space…
Blueprints - towards absolute arithmetic?
Oliver Lorscheid
One of the driving motivations to develop $\F_1$-geometry is the hope to translate Weil's proof of the Riemann hypothesis from positive characteristics to number fields, which migh…
Projective geometry for blueprints
Javier López Peña, Oliver Lorscheid
In this note, we generalize the Proj-construction from usual schemes to blue schemes. This yields the definition of projective space and projective varieties over a blueprint. In p…
The geometry of blueprints. Part II: Tits-Weyl models of algebraic groups
Oliver Lorscheid
This paper is dedicated to a problem raised by Jacquet Tits in 1956: the Weyl group of a Chevalley group should find an interpretation as a group over what is nowadays called $\mat…