Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2013 Abstract A quasi-smooth derived enhancement of a Deligne–Mumford stack 𝒳 naturally endows 𝒳 with a functorial perfect obstruction theory in the sense of Behrend–Fantechi. We apply this result to moduli of maps and perfect complexes on a smooth complex projective variety.
Timo Schürg +2 more
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Classical and Quantum Convolutional Codes Derived From Algebraic Geometry Codes [PDF]
IEEE Transactions on Communications, 2018 In this paper, we construct new families of classical convolutional codes (CCC's) and new families of quantum convolutional codes (QCC's). The CCC's are derived from (block) algebraic geometry (AG) codes. Furthermore, new families of CCC's are constructed by applying the techniques of puncturing, extending, expanding, and by the direct product code ...
Francisco Revson F. Pereira +2 more
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A note on Chern character, loop spaces and derived algebraic geometry
, 2008 In this note we present a work in progress whose main purpose is to establish a categorified version of sheaf theory. We present a notion of derived categorical sheaves, which is a categorified version of the notion of complexes of sheaves of modules on schemes, as well as its quasi-coherent and perfect versions.
Bertrand Toën, Gabriele Vezzosi
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Derived Algebraic Geometry V: Structured Spaces
, 2009 In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.
Jacob Lurie
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The AKSZ Construction in Derived Algebraic Geometry as an Extended Topological Field Theory
, 2021 We construct a family of oriented extended topological field theories using the AKSZ construction in derived algebraic geometry, which can be viewed as an algebraic and topological version of the classical AKSZ field theories that occur in physics. These have as their targets higher categories of symplectic derived stacks, with higher morphisms given ...
Damien Calaque +2 more
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ADM-like Hamiltonian formulation of gravity in the teleparallel geometry: derivation of constraint algebra [PDF]
General Relativity and Gravitation, 2013 We derive a new constraint algebra for a Hamiltonian formulation of the Teleparallel Equivalent of General Relativity treated as a theory of cotetrad fields on a spacetime. The algebra turns out to be closed.
Andrzej Okołów
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Derived algebraic geometry of 2d lattice Yang-Mills theory [PDF]
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Marco Benini +2 more
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An introduction to derived (algebraic) geometry [PDF]
Rendiconti di Matematica e delle Sue ApplicazioniMostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author.
Jon Eugster, Jonathan Pridham
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Algebraic foliations and derived geometry II: the Grothendieck-Riemann-Roch theorem
, 2020 This is the second of series of papers on the study of foliations in the setting of derived algebraic geometry based on the central notion of derived foliation. We introduce sheaf-like coefficients for derived foliations, called quasi-coherent crystals, and construct a certain sheaf of dg-algebras of differential operators along a given derived ...
Bertrand Toën, Gabriele Vezzosi
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Computation of aberration coefficients for plane-symmetric reflective optical systems using Lie algebraic methods [PDF]
EPJ Web of Conferences, 2022 The Lie algebraic method offers a systematic way to find aberration coefficients of any order for plane-symmetric reflective optical systems. The coefficients derived from the Lie method are in closed form and solely depend on the geometry of the optical
Barion Antonio +3 more
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