The six operations for sheaves on Artin stacks II: Adic coefficients

By Yves Laszlo, Martin Olsson. 2006

155 citations recorded by the source corpus.

. In this paper we develop a theory of Grothendieck’s six operations for adic constructible sheaves on Artin stacks continuing the study of the ﬁnite coeﬃcients case in [12].

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/64e6c0675430d027cb45617e727156434f7e2c14

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Citations in the corpus

Shtukas and the Taylor expansion of L-functions (II) (2015, methodology): “We use Db c(S) to denote the derived category of Q`-complexes for the étale topology of S, as defined in [17].”
Enhanced six operations and base change theorem for higher Artin stacks (2012, unknown): “In the most recent and general one [24] by Laszlo and Olsson on Artin stacks, a technical condition was imposed on the base scheme which excludes, for example, the spectra of certain fields1.”
A classical model for derived critical loci (2013, background): “Laszlo and Olsson [21, 22] study derived categories of constructible sheaves, and perverse sheaves, on Artin stacks, in more detail.”
Perverse coherent sheaves (2009, background): “Laszlo and Olsson extended cohomological descent to unbounded derived categories in [15]; the claims easily follow.”
Odds and Ends on Finite Group Actions and Traces (2010, methodology): “If S is affine and excellent and if all schemes of finite type over S has finite l-cohomological dimension, the construction of Db c(X , E) and of the corresponding six operations is done in [LO08].”
A duality formalism in the spirit of Grothendieck and Verdier (2011, unknown): “Hn ; x Q`/ is the bounded derived category [17] of the quotient stack Hn .”
A ‘Darboux theorem’ for shifted symplectic structures on derived Artin stacks, with applications (2013, methodology): “Olsson [29] rewrites the theory, correcting this mistake.”
Cohomological χ–independence for moduli of one-dimensional sheaves and moduli of Higgs bundles (2020, methodology): “From now on, we work with the derived category Dc(−,Ql) of constructible sheaves with Qlcoefficients for Artin stacks as in [29, 30].”
On the classification of rank-two representations of quasiprojective fundamental groups (2007, background): “In practice, in the cases we consider in this paper, X will often be the stack theoretical quotient of a smooth variety Z by an action of a finite group G.”
Motives with exceptional Galois groups and the inverse Galois problem (2011, background): “Motives with exceptional Galois groups simply D(X) to denote the derived category of constructible Q′ -complexes on X, as defined in [23, 24].”