A Tangent Category Perspective on Connections in Algebraic Geometry

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-12-11 DOI:10.1007/s10485-024-09796-7

G. S. H. Cruttwell, Jean-Simon Pacaud Lemay, Elias Vandenberg

引用次数: 0

Abstract

There is an abstract notion of connection in any tangent category. In this paper, we show that when applied to the tangent category of affine schemes, this recreates the classical notion of a connection on a module (and similarly, in the tangent category of schemes, this recreates the notion of connection on a quasi-coherent sheaf of modules). By contrast, we also show that in the tangent category of algebras, there are no non-trivial connections.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.