Mathematics - Research News

Frobenius split subvarieties pull back in almost all characteristics

 Mathematics - Research News
 05 January 2021
David E Speyer. Source: Journal of Commutative Algebra, Volume 12, Number 4, 573--579.Abstract: Let [math] and [math] be schemes of finite type over [math] and let [math] be a finite map. We show the following holds for all sufficiently large primes [math] : If [math] and [math] are any splittings...

$F$-pure threshold and height of quasihomogeneous polynomials

 Mathematics - Research News
 05 January 2021
Susanne Müller. Source: Journal of Commutative Algebra, Volume 12, Number 4, 559--572.Abstract: The aim of this paper is to give a connection between the [math] -pure threshold of a polynomial and the height of the corresponding Artin–Mazur formal group. For this, we consider a quasihomogeneous...

$\star$-super potent domains

 Mathematics - Research News
 05 January 2021
Evan Houston, Muhammad Zafrullah. Source: Journal of Commutative Algebra, Volume 12, Number 4, 489--507.Abstract: For a finite-type star operation [math] on a domain [math] , we say that [math] is [math] -super potent if each maximal [math] -ideal of [math] contains a finitely generated ideal...

A converse to a construction of Eisenbud–Shamash

 Mathematics - Research News
 05 January 2021
Petter A. Bergh, David A. Jorgensen, W. Frank Moore. Source: Journal of Commutative Algebra, Volume 12, Number 4, 467--477.Abstract: Let [math] be a commutative local Noetherian ring, [math] a [math] -regular sequence in [math] , and [math] . Given a complex of finitely generated free [math]...

On the sum of $z$-ideals in subrings of $C(X)$

 Mathematics - Research News
 05 January 2021
Fariborz Azarpanah, Mehdi Parsinia. Source: Journal of Commutative Algebra, Volume 12, Number 4, 459--466.Abstract: Let [math] be a Tychonoff space and [math] be an intermediate subalgebra of [math] , i.e., [math] . We show that such subrings are precisely absolutely convex subalgebras of [math] ....

Primitive Equations with half horizontal viscosity

 Mathematics - Research News
 12 November 2020
Martin Saal. Source: Advances in Differential Equations, Volume 25, Number 11/12, 651--685.Abstract: We consider the $3D$ primitive equations and show, that one does need less than horizontal viscosity to obtain a well-posedness result in Sobolev spaces. Furthermore, we will also investigate the...

Spectral identities and smoothing estimates for evolution operators

 Mathematics - Research News
 12 November 2020
Matania Ben-Artzi, Michael Ruzhansky, Mitsuru Sugimoto. Source: Advances in Differential Equations, Volume 25, Number 11/12, 627--650.Abstract: Smoothing (and decay) spacetime estimates are discussed for evolution groups of self-adjoint operators in an abstract setting. The basic assumption is the...

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