Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Miller, Lance Edward"'
Publikováno v:
Math. Nachr. 297 (2024), 783-802
In this article we address a question concerning nilpotent Frobenius actions on Rees algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke for Cohen-Macaulay singularities. This is achieved by introducing a depth-li
Externí odkaz:
http://arxiv.org/abs/2212.11374
Autor:
Buium, Alexandru, Miller, Lance Edward
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 connections were introduced and studied. In this paper arithmetic analogues of c
Externí odkaz:
http://arxiv.org/abs/2212.02697
This article concerns monomial ideals fixed by differential operators of affine semi-group rings over $\mathbb{C}$. We give a complete characterization of when this happens. Perhaps surprisingly, every monomial ideal is fixed by an infinite set of ho
Externí odkaz:
http://arxiv.org/abs/2212.02696
Autor:
Miller, Lance Edward, Buium, Alexandru
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 respect to several Frobenius elements in the absolute Galois group of a
Externí odkaz:
http://arxiv.org/abs/2202.02400
Autor:
Buium, Alexandru, Miller, Lance Edward
A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory solutions can be defined in algebraically closed p-adic fields. As an app
Externí odkaz:
http://arxiv.org/abs/2103.16627
Autor:
Maddox, Kyle, Miller, Lance Edward
We address explicit constructions of new variants of $F$-nilpotent singularities. In particular, we explore how (generalized) weakly $F$-nilpotent singularities behave under gluing, Segre products, Veronese subrings, and the formation of diagonal hyp
Externí odkaz:
http://arxiv.org/abs/2101.00365
Autor:
Buium, Alexandru, Miller, Lance Edward
Using arithmetic jet spaces, we attach perfectoid spaces to smooth schemes and to $\delta$-morphisms of smooth schemes. We also study perfectoid spaces attached to arithmetic differential equations defined by some of the remarkable $\delta$-morphisms
Externí odkaz:
http://arxiv.org/abs/1911.00113
Autor:
Buium, Alexandru, Miller, Lance Edward
We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solutions to these equations with coordinates in algebraically closed fiel
Externí odkaz:
http://arxiv.org/abs/1911.00112
We show that the log canonical threshold of a generic determinantal variety and its generic link are the same.
Comment: revision
Comment: revision
Externí odkaz:
http://arxiv.org/abs/1908.03892
Recently, Peeva and the second author constructed irreducible projective varieties with regularity much larger than their degree, yielding counterexamples to the Eisenbud-Goto Conjecture. Their construction involved two new ideas: Rees-like algebras
Externí odkaz:
http://arxiv.org/abs/1903.00973