Relevant bibliographies by topics / Koszul duality in Galois theory

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Koszul duality in Galois theory'

Author: Grafiati
Published: 9 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Koszul duality in Galois theory"

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Positselski, Leonid, and Alexander Vishik. "Koszul duality and Galois cohomology." Mathematical Research Letters 2, no. 6 (1995): 771–81. http://dx.doi.org/10.4310/mrl.1995.v2.n6.a8.

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Hirsh, Joseph, and Joan Millès. "Curved Koszul duality theory." Mathematische Annalen 354, no. 4 (2012): 1465–520. http://dx.doi.org/10.1007/s00208-011-0766-9.

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Mirković, Ivan, and Simon Riche. "Linear Koszul duality." Compositio Mathematica 146, no. 1 (2009): 233–58. http://dx.doi.org/10.1112/s0010437x09004357.

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AbstractIn this paper we construct, for F1 and F2 subbundles of a vector bundle E, a ‘Koszul duality’ equivalence between derived categories of 𝔾m-equivariant coherent(dg-)sheaves on the derived intersection $F_1 \rcap _E F_2$, and the corresponding derived intersection $F_1^{\perp } \rcap _{E^*} F_2^{\perp }$. We also propose applications to Hecke algebras.
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Riche, Simon, Wolfgang Soergel, and Geordie Williamson. "Modular Koszul duality." Compositio Mathematica 150, no. 2 (2013): 273–332. http://dx.doi.org/10.1112/s0010437x13007483.

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AbstractWe prove an analogue of Koszul duality for category$ \mathcal{O} $of a reductive group$G$in positive characteristic$\ell $larger than$1$plus the number of roots of$G$. However, there are no Koszul rings, and we do not prove an analogue of the Kazhdan–Lusztig conjectures in this context. The main technical result is the formality of the dg-algebra of extensions of parity sheaves on the flag variety if the characteristic of the coefficients is at least the number of roots of$G$plus$2$.
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Chuang, Joseph, Andrey Lazarev, and Wajid Mannan. "Koszul–Morita duality." Journal of Noncommutative Geometry 10, no. 4 (2016): 1541–57. http://dx.doi.org/10.4171/jncg/265.

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Beilinson, Alexander, Victor Ginzburg, and Wolfgang Soergel. "Koszul Duality Patterns in Representation Theory." Journal of the American Mathematical Society 9, no. 2 (1996): 473–527. http://dx.doi.org/10.1090/s0894-0347-96-00192-0.

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Etgü, Tolga, and Yankı Lekili. "Koszul duality patterns in Floer theory." Geometry & Topology 21, no. 6 (2017): 3313–89. http://dx.doi.org/10.2140/gt.2017.21.3313.

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Paquette, Natalie M., and Brian R. Williams. "Koszul duality in quantum field theory." Confluentes Mathematici 14, no. 2 (2023): 87–138. http://dx.doi.org/10.5802/cml.88.

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DOTSENKO, VLADIMIR, and BRUNO VALLETTE. "HIGHER KOSZUL DUALITY FOR ASSOCIATIVE ALGEBRAS." Glasgow Mathematical Journal 55, A (2013): 55–74. http://dx.doi.org/10.1017/s0017089513000505.

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AbstractWe present a unifying framework for the key concepts and results of higher Koszul duality theory for N-homogeneous algebras: the Koszul complex, the candidate for the space of syzygies and the higher operations on the Yoneda algebra. We give a universal description of the Koszul dual algebra under a new algebraic structure. For that we introduce a general notion: Gröbner bases for algebras over non-symmetric operads.
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Tu, Junwu. "Matrix factorizations via Koszul duality." Compositio Mathematica 150, no. 9 (2014): 1549–78. http://dx.doi.org/10.1112/s0010437x14007295.

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AbstractIn this paper we prove a version of curved Koszul duality for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathbb{Z}/2\mathbb{Z}$-graded curved coalgebras and their cobar differential graded algebras. A curved version of the homological perturbation lemma is also obtained as a useful technical tool for studying curved (co)algebras and precomplexes. The results of Koszul duality can be applied to study the category of m
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Dissertations / Theses on the topic "Koszul duality in Galois theory"

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QUADRELLI, CLAUDIO. "Cohomology of Absolute Galois Groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/56993.

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The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-p case, i.e., one would like to know which pro-p groups occur as maximal pro-p Galois groups, i.e., maximal pro-p quotients of absolute Galois groups. Indeed, pro-p groups are easier to deal with than general profinite groups, yet they carry a lot of information on the whole absolute Galois group. We define a new class of pro-p groups, called Bloch-K
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Cooper, Barrie. "Almost Koszul duality and rational conformal field theory." Thesis, University of Bath, 2007. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442883.

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Kelly, Jack. "Exact categories, Koszul duality, and derived analytic algebra." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:27064241-0ad3-49c3-9d7d-870d51fe110b.

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Recent work of Bambozzi, Ben-Bassat, and Kremnitzer suggests that derived analytic geometry over a valued field k can be modelled as geometry relative to the quasi-abelian category of Banach spaces, or rather its completion Ind(Ban<sub>k</sub>). In this thesis we develop a robust theory of homotopical algebra in Ch(E) for E any sufficiently 'nice' quasi-abelian, or even exact, category. Firstly we provide sufficient conditions on weakly idempotent complete exact categories E such that various categories of chain complexes in E are equipped with projective model structures. In particular we sho
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Kerkhoff, Sebastian. "A General Duality Theory for Clones." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-74783.

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In this thesis, we generalize clones (as well as their relational counterparts and the relationship between them) to categories. Based on this framework, we introduce a general duality theory for clones and apply it to obtain new results for clones on finite sets.
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Kerkhoff, Sebastian. "A General Galois Theory for Operations and Relations in Arbitrary Categories." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-73920.

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In this paper, we generalize the notions of polymorphisms and invariant relations to arbitrary categories. This leads us to a Galois connection that coincides with the classical case from universal algebra if the underlying category is the category of sets, but remains applicable no matter how the category is changed. In analogy to the situation in universal algebra, we characterize the Galois closed classes by local closures of clones of operations and local closures of what we will introduce as clones of (generalized) relations. Since the approach is built on purely category-theoretic proper
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Dehling, Malte. "Symmetric Homotopy Theory for Operads and Weak Lie 3-Algebras." Doctoral thesis, 2020. http://hdl.handle.net/21.11130/00-1735-0000-0005-1545-6.

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Book chapters on the topic "Koszul duality in Galois theory"

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Toda, Yukinobu. "Koszul Duality Equivalence." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_2.

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Soergel, Wolfgang. "Langlands’ Philosophy and Koszul Duality." In Algebra — Representation Theory. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0814-3_17.

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Kumar, Neeraj. "A Survey on Koszul Algebras and Koszul Duality." In Leavitt Path Algebras and Classical K-Theory. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1611-5_7.

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Toda, Yukinobu. "Categorical Wall-Crossing via Koszul Duality." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_5.

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Harari, David. "Poitou–Tate Duality." In Galois Cohomology and Class Field Theory. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43901-9_17.

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Harari, David. "The Tate Local Duality Theorem." In Galois Cohomology and Class Field Theory. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43901-9_10.

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Barbaresco, Frédéric. "Eidetic Reduction of Information Geometry Through Legendre Duality of Koszul Characteristic Function and Entropy: From Massieu–Duhem Potentials to Geometric Souriau Temperature and Balian Quantum Fisher Metric." In Geometric Theory of Information. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05317-2_7.

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Journal articles
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