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Autor:
Achinger, Piotr, Talpo, Mattia
Publikováno v:
Geom. Topol. 25 (2021) 1919-1978
We give two constructions of functorial topological realizations for schemes of finite type over the field $\mathbb{C}(\!(t)\!)$ of formal Laurent series with complex coefficients, with values in the homotopy category of spaces over the circle. The p
Externí odkaz:
http://arxiv.org/abs/1909.02903
We complete the program, initiated in [6], to compare the many different possible definitions of the underlying homotopy type of a log scheme. We show that, up to profinite completion, they all yield the same result, and thus arrive at an unambiguous
Externí odkaz:
http://arxiv.org/abs/1905.06243
Publikováno v:
J. Algebra 559 (2020), 1-32
We introduce preordered semi-orthogonal decompositions (psod-s) of dg-categories. We show that homotopy limits of dg-categories equipped with compatible psod-s carry a natural psod. This gives a way to glue semi-orthogonal decompositions along faithf
Externí odkaz:
http://arxiv.org/abs/1901.01257
We construct semi-orthogonal decompositions on triangulated categories of parabolic sheaves on certain kinds of logarithmic schemes. This provides a categorification of the decomposition theorems in Kummer flat K-theory due to Hagihara and Nizio{\l}.
Externí odkaz:
http://arxiv.org/abs/1803.06398
Autor:
Koppensteiner, Clemens, Talpo, Mattia
Publikováno v:
Advances in Mathematics 346 (2019), 510-545
We introduce the notion of a holonomic D-module on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In contrast to the classical case, the pushforward of a holonomic module along an open immersion
Externí odkaz:
http://arxiv.org/abs/1802.00732
Autor:
Talpo, Mattia
We define quasi-coherent parabolic sheaves with real weights on a fine saturated log analytic space, and explain how to interpret them as quasi-coherent sheaves of modules on its Kato-Nakayama space. This recovers the description as sheaves on root s
Externí odkaz:
http://arxiv.org/abs/1703.04777
Autor:
Talpo, Mattia, Vistoli, Angelo
We extend the formalism of "log spaces" of arXiv:1507.06752 to topoi equipped with a sheaf of monoids, and discuss Deligne--Faltings structures and root stacks in this context.
Comment: v2: final version, to appear in Boll. Unione Mat. Ital. arX
Comment: v2: final version, to appear in Boll. Unione Mat. Ital. arX
Externí odkaz:
http://arxiv.org/abs/1703.02663
Autor:
Pirisi, Roberto, Talpo, Mattia
We compute the class of the classifying stack of the exceptional algebraic group $G_2$ and of the spin groups $\mathrm{Spin}_7$ and $\mathrm{Spin}_8$ in the Grothendieck ring of stacks, and show that they are equal to the inverse of the class of the
Externí odkaz:
http://arxiv.org/abs/1702.02649
Publikováno v:
Compositio Math. 154 (2018) 2534-2585
We globalize the derived version of the McKay correspondence of Bridgeland-King-Reid, proven by Kawamata in the case of abelian quotient singularities, to certain log algebraic stacks with locally free log structure. The two sides of the corresponden
Externí odkaz:
http://arxiv.org/abs/1612.08961