Journal of the London Mathematical Society-Second Series最新文献

In this paper, we show the existence of uniform rational lc polytopes for foliations with functional boundaries in dimension $��⩽�3�$. As an application, we prove the global ACC for foliated threefolds with arbitrary DCC coefficients. We also provide applications on the accumulation points of lc thresholds of foliations in dimension $��⩽�3�$.

We consider the mixed local and nonlocal functionals with nonstandard growth

We consider the generalized parabolic Cahn–Hilliard equation

We classify all 2-blocks with abelian defect groups of rank 4 up to Morita equivalence. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. An application is that Broué's abelian defect group conjecture holds for all blocks under consideration here.

We demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible cardinal. As an application, relative to the existence of large cardinals, we construct a model of set theory in which there is a strongly inaccessible cardinal $�\kappa$ that is $�n$-$�d$-stationary for all $��n�\in �\omega �$ but not weakly compact. This is in sharp contrast to the situation in the constructible universe $�L$, where $�\kappa$ being $��(�n�+�1�)�$-$�d$-stationary is equivalent to $�\kappa$ being $�{\Pi }_n^1$-indescribable. We also show that it is consistent that there is a cardinal $��\kappa �⩽�2^{\omega }�$

By a classical theorem of Jordan, every faithful transitive action of a non-trivial finite group has a derangement (an element with no fixed points). The existence of derangements with additional properties has attracted much attention, especially for faithful primitive actions of almost simple groups. In this paper, we show that an almost simple group can have an element that is a derangement in every faithful primitive action, and we call these elements totally deranged. In fact, we classify the totally deranged elements of all almost simple groups, showing that an almost simple group $�G$ contains a totally deranged element only if the socle of $�G$ is $��{\mathrm{Sp}}_4��\left(�2^f�\right)��$ or $��P�{\Omega }_n^{+}��\left(�q�\right)��$ with $��n�=�2^l�⩾�8�$. Using this, we classify the invariable generating sets of a finite simple group $�G$ of the form $��\{�x�$

Let $��(�X�,�\Delta �)�$ be a projective klt pair, and $��f�:�X�\to �Y�$ a fibration to a smooth projective variety $�Y$ with strictly nef relative anti-log canonical divisor $��-�(�K_{�X�/�Y�}�+�\Delta �)�$. We prove that $�f$ is a locally trivial fibration with rationally connected fibres, and the base $�Y$ is a canonically polarized hyperbolic manifold. In particular, when $�Y$ is a single point, we establish that $�X$ is rationally connected. Moreover, when $��dim�X�=�3�$ and $��-�(�K_X�+�\Delta �)�$

We study the Bolker–Pacala–Dieckmann–Law (BPDL) model of population dynamics in the regime of large population density. The BPDL model is a particle system in which particles reproduce, move randomly in space and compete with each other locally. We rigorously prove global survival as well as a shape theorem describing the asymptotic spread of the population, when the population density is sufficiently large. In contrast to most previous studies, we allow the competition kernel to have an arbitrary, even infinite range, whence the term non-local competition. This makes the particle system non-monotone and of infinite-range dependence, meaning that the usual comparison arguments break down and have to be replaced by a more hands-on approach. Some ideas in the proof are inspired by works on the non-local Fisher-KPP equation, but the stochasticity of the model creates new difficulties.

Genus Theory is a classical feature of integral binary quadratic forms. Using the author's generalization of the well-known correspondence between quadratic form classes and ideal classes of quadratic algebras, we extend it to the case when quadratic forms are twisted and have coefficients in any principal ideal domain (PID) $�R$. When $��R�=�K�\left[�X�\right]�$, we show that the Genus Theory map is the quadratic form version of the 2-descent map on a certain hyperelliptic curve. As an application, we make a contribution to a question of Agboola and Pappas regarding a specialization problem of divisor classes on hyperelliptic curves. Under suitable assumptions, we prove that the set of nontrivial specializations has density 1.

In a compactly generated triangulated category, we introduce a class of tilting objects satisfying a certain purity condition. We call these the decent tilting objects and show that the tilting heart induced by any such object is equivalent to a category of contramodules over the endomorphism ring of the tilting object endowed with a natural linear topology. This extends the recent result for n-tilting modules by Positselski and Št'ovíček. In the setting of the derived category of modules over a ring, we show that the decent tilting complexes are precisely the silting complexes such that their character dual is cotilting. The hearts of cotilting complexes of cofinite type turn out to be equivalent to the category of discrete modules with respect to the same topological ring. Finally, we provide a kind of Morita theory in this setting: Decent tilting complexes correspond to pairs consisting of a tilting and a cotilting-derived equivalence as described above tied together by a tensor compatibility condition.