Locally Semialgebraic Superspaces and Nash Supermanifolds

Autor:	Can, Mahir Bilen
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	In this article, we present a novel theory of locally semialgebraic superspaces along with Nash supermanifolds. By adapting Batchelor's theorem to our framework, we show that all locally semialgebraic superspaces and affine Nash supermanifolds can be derived from appropriate vector bundles. Our analysis of Nash supermanifolds involves an investigation of a topology, where closed sets are defined by Nash subsets. Within this context, we establish the softness of the structure sheaf for an affine Nash manifold. Moreover, we establish that under this topology, the higher cohomology of quasi-coherent sheaves on an affine Nash manifold vanishes completely. These results open up new directions for cohomological studies on Nash manifolds. Comment: To appear in Contemporary Mathematics of the AMS
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.16949 Zobrazit plný text záznamu View this record from Arxiv