Zobrazeno 1 - 10
of 168
pro vyhledávání: '"Buium, Alexandru"'
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
Autor:
Buium, Alexandru, Vasiu, Adrian
Let $p$ be a prime, let $N\geq 3$ be an integer prime to $p$, let $R$ be the ring of $p$-typical Witt vectors with coefficients in an algebraic closure of $\mathbb F_p$, and consider the correspondence $\mathcal A'_{g,1,N,R}\rightrightarrows \mathcal
Externí odkaz:
http://arxiv.org/abs/2208.00286
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:
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