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Silting and cosilting classes in derived categories
An important result in tilting theory states that a class of modules over a
ring is a tilting class if and only if it is the Ext-orthogonal class to a set
of compact modules of bounded projective dimension. Moreover, cotilting classes
are precisely the resolving and definable subcategories of the module category
whose Ext-orthogonal class has bounded injective dimension.
In this article, we prove a derived counterpart of the statements above in
the context of silting theory. Silting and cosilting complexes in the derived
category of a ring generalise tilting and cotilting modules. They give rise to
subcategories of the derived category, called silting and cosilting classes,
which are part of both a t-structure and a co-t-structure. We characterise
these subcategories: silting classes are precisely those which are intermediate
and Ext-orthogonal classes to a set of compact objects, and cosilting classes
are precisely the cosuspended, definable and co-intermediate subcategories of
the derived category
Rotating effects on the scalar field in the cosmic string spacetime, in the spacetime with space-like dislocation and in the spacetime with a spiral dislocation
In the interface between general relativity and relativistic quantum
mechanics, we analyse rotating effects on the scalar field subject to a
hard-wall confining potential. We consider three different scenarios of general
relativity given by the cosmic string spacetime, the spacetime with space-like
dislocation and the spacetime with a spiral dislocation. Then, by searching for
a discrete spectrum of energy, we analyse analogues effects of the
Aharonov-Bohm effect for bound states and the Sagnac effect.Comment: 12 pages, no figure. To be published in The European Physical Journal
Torsion pairs in silting theory
In the setting of compactly generated triangulated categories, we show that
the heart of a (co)silting t-structure is a Grothendieck category if and only
if the (co)silting object satisfies a purity assumption. Moreover, in the
cosilting case the previous conditions are related to the coaisle of the
t-structure being a definable subcategory. If we further assume our
triangulated category to be algebraic, it follows that the heart of any
nondegenerate compactly generated t-structure is a Grothendieck category.Comment: Changes in v2: new Proposition 4.5, weaker assumptions in Lemma 4.8
and some minor changes throughou
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