2024/02/23 by Nidhi Gupta, Gupta, Nidhi
Computer Science · Mathematics · #14F42 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2402.15329
openalex publication_date 2024/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any sheaf of sets \mathcal F on Sm/k, it is well known that the universal \mathbb A1-invariant quotient of \mathcal F is given as the colimit of sheaves \mathcal Sn(\mathcal F) where \mathcal S(F) is the sheaf of naive \mathbb A1-connected components of \mathcal F. We show that these infinite iterations of naive \mathbb A1-connected components in the construction of universal \mathbb A1-invariant quotient for a scheme are certainly required. For every n, we construct an \mathbb A1-connected variety Xn such that \mathcal Sn(Xn)≠ \mathcal Sn+1(Xn) and \mathcal Sn+2(Xn)=*.