Results 11 to 20 of about 347 (81)
Algebraic theories of power operations
Journal of Topology, Volume 16, Issue 4, Page 1543-1640, December 2023., 2023 Abstract We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well‐behaved theories of power operations for E∞$\mathbb {E}_\infty$ ring spectra.
William Balderrama
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Perfectoid Shimura varieties and the Calegari–Emerton conjectures
Journal of the London Mathematical Society, Volume 108, Issue 5, Page 1954-2000, November 2023., 2023 Abstract We prove many new cases of a conjecture of Calegari–Emerton describing the qualitative properties of completed cohomology. The heart of our argument is a careful inductive analysis of completed cohomology on the Borel–Serre boundary. As a key input to this induction, we prove a new perfectoidness result for towers of minimally compactified ...
David Hansen, Christian Johansson
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Differential graded Koszul duality: An introductory survey
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1551-1640, August 2023., 2023 Abstract This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011), no. 996, vi+133. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG‐algebras and curved DG‐coalgebras, as ...
Leonid Positselski
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A survey on deformations, cohomologies and homotopies of relative Rota–Baxter Lie algebras
Bulletin of the London Mathematical Society, Volume 54, Issue 6, Page 2045-2065, December 2022., 2022 Abstract In this paper, we review deformation, cohomology and homotopy theories of relative Rota–Baxter (RB$\mathsf {RB}$) Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived brackets, one can obtain an L∞$L_\infty$‐algebra whose Maurer–Cartan elements are relative RB$\mathsf {RB}$ Lie algebras.
Yunhe Sheng
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On the Grothendieck–Serre conjecture for classical groups
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 2884-2926, December 2022., 2022 Abstract We prove some new cases of the Grothendieck–Serre conjecture for classical groups. This is based on a new construction of the Gersten–Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue maps; the complex is shown to be exact when the ring is of dimension ⩽2$\leqslant 2$ (or ⩽
Eva Bayer‐Fluckiger +2 more
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Moduli problems for operadic algebras
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3450-3544, December 2022., 2022 Abstract A theorem of Pridham and Lurie provides an equivalence between formal moduli problems and Lie algebras in characteristic zero. We prove a generalization of this correspondence, relating formal moduli problems parametrized by algebras over a Koszul operad to algebras over its Koszul dual operad. In particular, when the Lie algebra associated to
Damien Calaque +2 more
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Hypersurface singularities with monomial Jacobian ideal
Bulletin of the London Mathematical Society, Volume 54, Issue 3, Page 1067-1081, June 2022., 2022 Abstract We show that every convergent power series with monomial extended Jacobian ideal is right equivalent to a Thom–Sebastiani polynomial. This solves a problem posed by Hauser and Schicho. On the combinatorial side, we introduce a notion of Jacobian semigroup ideal involving a transversal matroid.
Raul Epure, Mathias Schulze
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Homotopy Transfer and Effective Field Theory I: Tree‐level
Fortschritte der Physik, Volume 70, Issue 2-3, March 2022., 2022 Abstract We use the dictionary between general field theories and strongly homotopy algebras to provide an algebraic formulation of the procedure of integrating out of degrees of freedom in terms of homotopy transfer. This includes more general effective theories in which some massive modes are kept while other modes of a comparable mass scale are ...
Alex S. Arvanitakis +3 more
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A Class of Koszul Algebra and Some Homological Invariants through Circulant Matrices and Cycles
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Recent advances in graph theory, linear algebra, and commutative algebra render us to tackle problems in one bough of mathematics with assistance and guidance from others. We will elaborate foremost and conceptually fathomless homological invariants inextricably linked with circulant matrices and cycles through various path lengths in this article, as ...
Muhammed Nadeem +6 more
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Fortschritte der Physik, Volume 69, Issue 11-12, December 2021., 2021 Abstract We consider supersymmetry in five dimensions, where the fermionic parameters are a 2‐form under . Supermultiplets are investigated using the pure spinor superfield formalism, and are found to be closely related to infinite‐dimensional extensions of the supersymmetry algebra: the Borcherds superalgebra , the tensor hierarchy algebra and the ...
Martin Cederwall
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