Chromatic homotopy theory is algebraic when p &gt; n2 + n + 1

Pstrągowski, Piotr

doi:10.1016/j.aim.2021.107958

Cited by 7 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a related result, Pstragowski [Pst21] shows that for 2p − 2 > 2(n 2 + n) and k = 2p − 2 − n 2 − n there is an equivalence…”

Section: Landweber Exact Hopf Algebroids and The Moduli Stack Of Form...mentioning

confidence: 92%

“…Here D per (Comod E0E ) denotes the ∞-category of quasi-periodic E 0 E-comodules for a 2-periodic Landweber exact cohomology theory E of height n (essentially) first introduced by Franke [Fra96]. Alternatively, this is the derived category of differential E * E-comodules, where a differential E * E-comodule is a pair (M, d) consisting of an E * E-comodule M and d : M → M is a map of comodules of degree 1 satisfying d 2 = 0 (this is the approach taken in [Pst21], and the equivalence of the two approaches is given in [Pst21, Proposition 3.3]).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Invertible objects in Franke's comodule categories

Heard¹

2022

Preprint

View full text Add to dashboard Cite

We study the Picard group of Franke's category of quasi-periodic E 0 E-comodules for E a 2-periodic Landweber exact cohomology theory of height n such as Morava E-theory, showing that for 2p − 2 > n 2 + n, this group is infinite cyclic, generated by the suspension of the unit. This is analogous to, but independent of, the corresponding calculations by Hovey and Sadofsky in the E-local stable homotopy category. We also give a computation of the Picard group of In-complete quasi-periodic E 0 E-comodules when E is Morava E-theory, as studied by Barthel-Schlank-Stapleton for 2p − 2 ≥ n 2 and p − 1 n, and compare this to the Picard group of the K(n)-local stable homotopy category, showing that they agree up to extension.

show abstract

“…In a related result, Pstragowski [Pst21] shows that for 2p − 2 > 2(n 2 + n) and k = 2p − 2 − n 2 − n there is an equivalence…”

Section: Landweber Exact Hopf Algebroids and The Moduli Stack Of Form...mentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Invertible objects in Franke's comodule categories

Heard¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Theorems on uniqueness of enhancements exist in the literature for triangulated categories coming from algebraic geometry [14,32] or algebraic topology [49,50,52]. Nevertheless, enhancements are in general not unique when they exist; see [26,47,48] for some algebraic examples and [20], [49, §2.1], [41,42] for topologically flavored examples.…”

Section: Introductionmentioning

confidence: 99%

Enhanced Finite Triangulated Categories

Muro¹

2020

J. Inst. Math. Jussieu

View full text Add to dashboard Cite

show abstract

On conjectures of Hovey–Strickland and Chai

Barthel

Heard

Naumann

2022

Sel. Math. New Ser.

View full text Add to dashboard Cite

We prove the height two case of a conjecture of Hovey and Strickland that provides a K(n)-local analogue of the Hopkins–Smith thick subcategory theorem. Our approach first reduces the general conjecture to a problem in arithmetic geometry posed by Chai. We then use the Gross–Hopkins period map to verify Chai’s Hope at height two and all primes. Along the way, we show that the graded commutative ring of completed cooperations for Morava E-theory is coherent, and that every finitely generated Morava module can be realized by a K(n)-local spectrum as long as $$2p-2>n^2+n$$ 2 p - 2 > n 2 + n . Finally, we deduce consequences of our results for descent of Balmer spectra.

show abstract

Chromatic homotopy theory is algebraic when p > n2 + n + 1

Cited by 7 publications

References 14 publications

Invertible objects in Franke's comodule categories

Invertible objects in Franke's comodule categories

Enhanced Finite Triangulated Categories

On conjectures of Hovey–Strickland and Chai

Contact Info

Product

Resources

About

Chromatic homotopy theory is algebraic when p > n2 + n + 1

Cited by 7 publications

References 14 publications

Invertible objects in Franke's comodule categories

Invertible objects in Franke's comodule categories

Enhanced Finite Triangulated Categories

On conjectures of Hovey–Strickland and Chai

Contact Info

Product

Resources

About

Chromatic homotopy theory is algebraic when p > n2 + n + 1