25 citations · 33 across the 8 of their papers we have counts for
13 papers
Projected distances for multi-parameter persistence modules
Nicolas Berkouk, Francois Petit
Relying on sheaf theory, we introduce the notions of projected barcodes and projected distances for multi-parameter persistence modules. Projected barcodes are defined as derived p…
A property of the interleaving distance for sheaves
Francois Petit, Pierre Schapira, Lukas Waas
Let be a real analytic manifold endowed with a distance satisfying suitable properties and let be a field. In [PS20], the authors construct a pseudo-distance on th…
Thickening of the diagonal and interleaving distance
Francois Petit, Pierre Schapira
Given a topological space , a thickening kernel is a monoidal presheaf on with values in the monoidal category of derived kernels on . A bi-thickenin…
Integral representation theorems for DQ-modules
David Gepner, Francois Petit
We identify the type of -linear structure inherent in the -categories which arise in the theory of Deformation Quantization modules. Using this structu…
Ephemeral persistence modules and distance comparison
Nicolas Berkouk, Francois Petit
We provide a definition of ephemeral multi-persistent modules and prove that the quotient of persistent modules by the ephemeral ones is equivalent to the category of -sheaves.…
Holomorphic Frobenius actions for DQ-modules
Francois Petit
Given a complex manifold endowed with a -action and a DQ-algebra equipped with a compatible holomorphic Frobenius action (F-action), we prove that if the $\mathb…
Tempered subanalytic topology on algebraic varieties
Francois Petit
On a smooth algebraic variety over , we build the tempered subanalytic and Stein tempered subanalytic sites. We construct the sheaf of holomorphic functions tempered at…
Quantization of spectral curves and DQ-modules
Francois Petit
Given an holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, we construct a DQ-module supported by the spectral curve associated to this bundle. Then,…
The Codimension-Three conjecture for holonomic DQ-modules
Francois Petit
We prove an analogue for holonomic DQ-modules of the codimension-three conjecture for microdifferential modules recently proved by Kashiwara and Vilonen. Our result states that any…
Fourier-Mukai transform in the quantized setting
Francois Petit
We prove that a coherent DQ-kernel induces an equivalence between the derived categories of DQ-modules with coherent cohomology if and only if the graded commutative kernel associa…
The Lefschetz-Lunts formula for deformation quantization modules
Francois Petit
We adapt to the case of deformation quantization modules a formula of V. Lunts who calculates the trace of a kernel acting on Hochschild homology.
DG Affinity of DQ-modules
Francois Petit
In this paper, we prove the dg affinity of formal deformation algebroid stacks over complex smooth algebraic varieties. For that purpose, we introduce the triangulated category of…
A Riemann-Roch Theorem for dg Algebras
Francois Petit
Given a smooth proper dg-algebra , a perfect dg -module , and an endomorphism of , we define the Hochschild class of the pair with values in the Hochschild…