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spectral group scheme

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Idea

A spectral group scheme is a group scheme in E-∞ geometry. In the affine case then the formal dual notion is a Hopf E-∞ algebra.

(Integrate comment here about smooth and flat versions.)

Example

  • GLGL: Consider RR an E-∞ ring, CAlg RCAlg_R, the ∞-category of RR-algebras, Mod RMod_R an ∞-category of RR-modules. Let Sym RSym_R be left adjoint to the forgetful functor CAlg RMod RCAlg_R \to Mod_R. Set M n,R=SpecSym REnd R(R n)M_{n,R} = Spec Sym_R End_R(R^{\oplus n}), a spectral monoid scheme which represents REnd R(R n)R \mapsto End_R(R^{\oplus n}). Let GL n,RGL_{n,R} be the spectral group scheme obtained by inverting the determinant element in π oM n,R\pi_o M_{n,R} (Ohara).

References

  • Mariko Ohara, On the K-theory of finitely generated projective modules over a spectral ring, slide 27 of slides.

Last revised on December 29, 2016 at 06:34:08. See the history of this page for a list of all contributions to it.