Related papers: Companions on Artin stacks

In this article we extend Deligne's construction of Grothendieck's six operations on the derived category of torsion sheaves over the \'etale site of a scheme for morphisms of finite type to a larger class of morphisms. This class includes…

We use Morse theory to prove that the Lefschetz Hyperplane Theorem holds for compact smooth Deligne-Mumford stacks over the site of complex manifolds. For $Z \subset X$ a hyperplane section, $X$ can be obtained from $Z$ by a sequence of…

We prove that every $0$-shifted symplectic structure on a derived Artin $n$-stack admits a curved $A_{\infty}$ deformation quantisation. The classical method of quantising smooth varieties via quantisations of affine space does not apply in…

As already observed by Gabriel, coherent sheaves on schemes obtained by gluing affine open subsets can be described by a simple gluing construction. An example due to Ferrand shows that this fails in general for pushouts along closed…

This paper presents a survey on formal moduli problems. It starts with an introduction to pointed formal moduli problems and a sketch of proof of a Theorem (independently proven by Lurie and Pridham) which gives a precise mathematical…

We present a Langlands dual realization of the putative category of affine character sheaves. Namely, we calculate the categorical center and trace (also known as the Drinfeld center and trace, or categorical Hochschild cohomology and…

We prove Arnol'd's three cusps conjecture about the front of Legendrian curves in the projectivized cotangent bundle of the $2$-sphere. We use the microlocal theory of sheaves of Kashiwara and Schapira and study the derived category of…

Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…

We characterize contractible curves on proper normal algebraic surfaces in terms of complementary Weil divisors. Using this we generalize the classical criteria of Castelnuovo and Artin. As application we derive a finiteness result on…

If $X$ is a smooth projective variety over ${\mathbb R}$, the Hodge ${\mathcal D}$-conjecture of Beilinson asserts the surjectivity of the regulator map to Deligne cohomology with real coefficients. It is known to be false in general but is…

For a toric Deligne-Mumford (DM) stack, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism on a two-dimensional toric DM stack, we show that the push-forward of the structure sheaf generates the…

We first introduce global arithmetic cohomology groups for quasi-coherent sheaves on arithmetic varieties, adopting an adelic approach. Then, we establish fundamental properties, such as topological duality and inductive long exact…

We classify the Deligne-Mumford stacks M compactifying the moduli space of smooth $n$-pointed curves of genus one under the condition that the points of M represent Gorenstein curves with distinct markings. This classification uncovers new…

We formulate and study a torsion analogue of the weight-monodromy conjecture for a proper smooth scheme over a non-archimedean local field. We prove it for proper smooth schemes over equal characteristic non-archimedean local fields,…

We introduce the notion of extension of 1-motives. Using the dictionary between strictly commutative Picard stacks and complexes of abelian sheaves concentrated in degrees -1 and 0, we check that an extension of 1-motives induces an…

We introduce a conjecture on Virasoro constraints for the moduli space of stable sheaves on a smooth projective surface. These generalise the Virasoro constraints on the Hilbert scheme of a surface found by Moreira (arXiv:2008.13746) and…

We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective…

We introduce a method of finding large non-positively curved subcomplexes in certain spherical Deligne complexes, which is effective for studying fillings of certain 6-cycles in spherical Deligne complexes. As applications, we show the…

We show that the automorphism group of Drinfeld's half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the sense of Berkovich over the finite field…

We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic p (as defined by Abramovich, Olsson, and Vistoli) which lift mod p^2 degenerates. We push the result to the coarse spaces of such…