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math.NT2022
Arithmetic differential geometry in the arithmetic PDE setting II: curvature and cohomology
Alexandru Buium, Lance Edward Miller
This is the second paper in a series devoted to developing an arithmetic PDE analogue of Riemannian geometry. In Part 1 arithmetic PDE analogues of Levi-Civita and Chern connection…
math.AC2022
Differentially fixed ideals in toric varieties
Lance Edward Miller, William D. Taylor, Janet Vassilev
This article concerns monomial ideals fixed by differential operators of affine semi-group rings over . We give a complete characterization of when this happens. Perhap…
math.NT2022
Arithmetic differential geometry in the arithmetic PDE setting, I: connections
Lance Edward Miller, Alexandru Buium
This is the first in a series on papers developing an arithmetic PDE analogue of Riemannian geometry. The role of partial derivatives is played by Fermat quotient operations with r…