Relevant bibliographies by topics / Koszul duality in Galois theory

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

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Published: 9 March 2023

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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 (January 3, 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 (December 16, 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 (December 13, 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 (August 31, 2017): 3313–89. http://dx.doi.org/10.2140/gt.2017.21.3313.

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Tu, Junwu. "Matrix factorizations via Koszul duality." Compositio Mathematica 150, no. 9 (July 17, 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 matrix factorizations $\mathsf{MF}(R,W)$. We show how Dyckerhoff’s generating results fit into the framework of curved Koszul duality theory. This enables us to clarify the relationship between the Borel–Moore Hochschild homology of curved (co)algebras and the ordinary Hochschild homology of the category $\mathsf{MF}(R,W)$. Similar results are also obtained in the orbifold case and in the graded case.
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Bodzenta, Agnieszka, and Julian Külshammer. "Ringel duality as an instance of Koszul duality." Journal of Algebra 506 (July 2018): 129–87. http://dx.doi.org/10.1016/j.jalgebra.2018.03.025.

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DOTSENKO, VLADIMIR, and BRUNO VALLETTE. "HIGHER KOSZUL DUALITY FOR ASSOCIATIVE ALGEBRAS." Glasgow Mathematical Journal 55, A (October 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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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-Kato pro-p group, whose Galois cohomology satisfies the consequences of the Bloch-Kato conjecture. Also we introduce the notion of cyclotomic orientation for a pro-p group. With this approach, we are able to recover new substantial information about the structure of maximal pro-p Galois groups, and in particular on theta-abelian pro-p groups, which represent the "upper bound" of such groups. Also, we study the restricted Lie algebra and the universal envelope induced by the Zassenhaus filtration of a maximal pro-p Galois group, and their relations with Galois cohomology via Koszul duality. Altogether, this thesis provides a rather new approach to maximal pro-p Galois groups, besides new substantial results.
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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(Bank). 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 show that as soon as E has enough projectives, the category Ch+(E) of bounded below complexes is equipped with a projective model structure. In the case that E also admits all kernels we show that it is also true of Ch≥0(E), and that a generalisation of the Dold-Kan correspondence holds. Supplementing the existence of kernels with a condition on the existence and exactness of certain direct limit functors guarantees that the category of unbounded chain complexes Ch(E) also admits a projective model structure. When E is monoidal we also examine when these model structures are monoidal. We then develop the homotopy theory of algebras in Ch(E). In particular we show, under very general conditions, that categories of operadic algebras in Ch(E) can be equipped with transferred model structures. Specialising to quasi-abelian categories we prove our main theorem, which is a vast generalisation of Koszul duality. We conclude by defining analytic extensions of the Koszul dual of a Lie algebra in Ind(Bank).
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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 properties, we will also discuss the dualization of our notions.
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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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Books on the topic "Koszul duality in Galois theory"

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Dualities on Generalized Koszul Algebras (Memoirs of the American Mathematical Society, No. 754). American Mathematical Society, 2002.

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

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Soergel, Wolfgang. "Langlands’ Philosophy and Koszul Duality." In Algebra — Representation Theory, 379–414. Dordrecht: 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, 157–76. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1611-5_7.

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Harari, David. "Poitou–Tate Duality." In Galois Cohomology and Class Field Theory, 259–78. Cham: 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, 131–43. Cham: 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, 141–217. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05317-2_7.

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