The C2–spectrum Tmf1(3) and its invertible modules

Hill, Michael A.; Meier, Lennart

doi:10.2140/agt.2017.17.1953

Cited by 40 publications

(48 citation statements)

References 54 publications

(57 reference statements)

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“…In this section we give a brief introduction to the category of C 2 -equivariant spectra. For a more detailed discussion, one can see the appendix of [10], or for a slightly shorter introduction, see [11,Section 2].…”

Section: The C 2 -Equivariant Homotopy Categorymentioning

confidence: 99%

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On equivariant and motivic slices

Heard

2019

Algebr. Geom. Topol.

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Let k be a field with a real embedding. We compare the motivic slice filtration of a motivic spectrum over Spec(k) with the C 2 -equivariant slice filtration of its equivariant Betti realization, giving conditions under which realization induces an equivalence between the associated slice towers. In particular, we show that, up to reindexing, the towers agree for all spectra obtained from localized quotients of MGL and MR, and for motivic Landweber exact spectra and their realizations. As a consequence, we deduce that equivariant spectra obtained from localized quotients of MR are even in the sense of Hill-Meier, and give a computation of the slice spectral sequence converging to π * , * BP n /2 for 1 ≤ n ≤ ∞.Published: XX Xxxember 20XX

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Section: The C 2 -Equivariant Homotopy Categorymentioning

confidence: 99%

“…Because of this, Hill and Meier [11] introduced the notion of even and strongly even C 2equivariant spectra.…”

Section: Remark 52mentioning

confidence: 99%

On equivariant and motivic slices

Heard

2019

Algebr. Geom. Topol.

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“…For the original case of λ = (4, 6), the presence of strictly semistable points inside P( Λ) prevents us from obtaining a proper moduli stack compactifying the moduli stack of stable Weierstrass fibrations. On the other hand, we note that the moduli stack M 1,1 [Γ 1 (3)] of generalized elliptic curves with [Γ 1 (3)]-level structure has an isomorphism M 1,1 [Γ 1 (3)] ∼ = P(1, 3) as in [HMe,Proposition 4.5] through the equation…”

Section: Methods and Techniquesmentioning

confidence: 99%

Arithmetic geometry of the moduli stack of Weierstrass fibrations over $\mathbb{P}^1$

Park¹,

Schmitt²

2021

Preprint

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Coarse moduli spaces of Weierstrass fibrations over the (unparameterized) projective line were constructed by the classical work of [Miranda] using Geometric Invariant Theory. In our paper, we extend this treatment by using results of [Romagny] regarding group actions on stacks to give an explicit construction of the moduli stack W n of Weierstrass fibrations over an unparameterized P 1 with discriminant degree 12n and a section. We show that it is a smooth algebraic stack and prove that for n ≥ 2, the open substack W min,n of minimal Weierstrass fibrations is a separated Deligne-Mumford stack over any base field K with char(K) = 2, 3 and ∤ n. Arithmetically, for the moduli stack W sf,n of stable Weierstrass fibrations, we determine its motive in the Grothendieck ring of stacks to be {W sf,n } = L 10n−2 in the case that n is odd, which results in its weighted point count to be # q (W sf,n ) = q 10n−2 over F q . In the appendix, we show how our methods can be applied similarly to the classical work of [Silverman] on coarse moduli spaces of self-maps of the projective line, allowing us to construct the natural moduli stack and to compute its motive.

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“…Given Γ ′ ⊂ Γ ⊂ Γ 0 (n) with Γ ′ tame with respect to Z S and Γ/Γ ′ ∼ = C 2 , we can extend our previous definition by defining tmf(Γ) S as tmf(Γ ′ ) C 2 S (so e.g. tmf 0 (3) = tmf 1 (3) C 2 as in [HM17]). If Γ itself is already tame, then 2 ∈ S. One then easily computes (e.g.…”

Section: The C 2 -Equivariant Argumentmentioning

confidence: 99%