An Algebraic characterization of the affine three space in arbitrary characteristic

2023/08/10 by Krishna, P. M. S. Sai
#13A50 #13B25 #13N15 #14R10 #14R20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.05424

Abstract

We give an algebraic characterization of the affine 3-space over an algebraically closed field of arbitrary characteristic. We use this characterization to reformulate the following question. Let A=k[X, Y, Z, T]/(XY+Z^pe+T+T^sp) where p^e\nmid sp, sp\nmid p^e, e, s≥ 1 and k is an algebraically closed field of positive characteristic p. Is A= k^[3]? We prove some results on ML and ML^* invariants and use them to prove a special case of the strong cancellation of k^[2].

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