35 citations · 83 across the 12 of their papers we have counts for
18 papers · 1 filter
The log homotopy exact sequence
Mattia Talpo
We show exactness of the homotopy sequence for the logarithmic fundamental group in the case of log smooth, finitely presented, proper and saturated morphisms of fs log schemes ove…
Betti realization of varieties defined by formal Laurent series
Piotr Achinger, Mattia Talpo
We give two constructions of functorial topological realizations for schemes of finite type over the field of formal Laurent series with complex coefficients,…
On the profinite homotopy type of log schemes
David Carchedi, Sarah Scherotzke, Nicolò Sibilla +1
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 complet…
Gluing semi-orthogonal decompositions
Sarah Scherotzke, Nicolò Sibilla, Mattia Talpo
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…
Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes
Sarah Scherotzke, Nicolò Sibilla, Mattia Talpo
We construct semi-orthogonal decompositions on triangulated categories of parabolic sheaves on certain kinds of logarithmic schemes. This provides a categorification of the decompo…
Holonomic and perverse logarithmic D-modules
Clemens Koppensteiner, Mattia Talpo
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 classic…
Parabolic sheaves with real weights as sheaves on the Kato-Nakayama space
Mattia Talpo
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 K…
A general formalism for logarithmic structures
Mattia Talpo, Angelo Vistoli
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.
On the motivic class of the classifying stack of and the spin groups
Roberto Pirisi, Mattia Talpo
We compute the class of the classifying stack of the exceptional algebraic group and of the spin groups and in the Grothendieck ring of st…
On a logarithmic version of the derived McKay correspondence
Sarah Scherotzke, Nicolò Sibilla, Mattia Talpo
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 sta…
Logarithmic Picard groups, chip firing, and the combinatorial rank
Tyler Foster, Dhruv Ranganathan, Mattia Talpo +1
Illusie has suggested that one should think of the classifying group of -torsors on a logarithmically smooth curve over a standard logarithmic point as a logarithmic…
The Kato-Nakayama space as a transcendental root stack
Mattia Talpo, Angelo Vistoli
We give a functorial description of the Kato-Nakayama space of a fine saturated log analytic space that is similar in spirit to the functorial description of root stacks. As a cons…
The motivic class of the classifying stack of the special orthogonal group
Mattia Talpo, Angelo Vistoli
We compute the class of the classifying stack of the special orthogonal group in the Grothendieck ring of stacks, and check that it is equal to the multiplicative inverse of the cl…
Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes
David Carchedi, Sarah Scherotzke, Nicolò Sibilla +1
For a log scheme locally of finite type over , a natural candidate for its profinite homotopy type is the profinite completion of its Kato-Nakayama space. Alternatively…
Moduli of parabolic sheaves on a polarized logarithmic scheme
Mattia Talpo
We generalize the construction of moduli spaces of parabolic sheaves given by Maruyama and Yokogawa in [MY92] to the case of a projective fine saturated log scheme with a fixed glo…
Infinite root stacks and quasi-coherent sheaves on logarithmic schemes
Mattia Talpo, Angelo Vistoli
We define and study infinite root stacks of fine and saturated logarithmic schemes, a limit version of the root stacks introduced by Niels Borne and the second author. We show in p…
Stacks of uniform cyclic covers of curves and their Picard groups
Flavia Poma, Mattia Talpo, Fabio Tonini
We study the stack B_{h,g,n} of uniform cyclic covers of degree n between smooth curves of genus h and g and, for h >> g, present it as an open substack of a vector bundle over the…
Deformation theory from the point of view of fibered categories
Mattia Talpo, Angelo Vistoli
We give an exposition of the formal aspects of deformation theory in the language of fibered categories, instead of the more traditional one of functors. The main concepts are that…