To a “stable homotopy theory” (a presentable, symmetric monoidal stable ∞-category), we naturally associate a category of finite étale algebra objects and, using Grothendieck's categorical machine, a ...profinite group that we call the Galois group. We then calculate the Galois groups in several examples. For instance, we show that the Galois group of the periodic E∞-algebra of topological modular forms is trivial and that the Galois group of K(n)-local stable homotopy theory is an extended version of the Morava stabilizer group. We also describe the Galois group of the stable module category of a finite group. A fundamental idea throughout is the purely categorical notion of a “descendable” algebra object and an associated analog of faithfully flat descent in this context.
The primary goal of this paper is to identify syntomic complexes with the p-adic étale Tate twists of Geisser–Sato–Schneider on regular p-torsion-free schemes. Our methods apply naturally to a ...broader class of schemes that we call ‘F-smooth’. The F-smoothness of regular schemes leads to new results on the absolute prismatic cohomology of regular schemes.
A short proof of telescopic Tate vanishing CLAUSEN, DUSTIN; MATHEW, AKHIL
Proceedings of the American Mathematical Society,
12/2017, Letnik:
145, Številka:
12
Journal Article
Recenzirano
Odprti dostop
We give a short proof of a theorem of Kuhn that Tate constructions for finite group actions vanish in telescopically localized stable homotopy theory. In particular, we observe that Kuhn's theorem is ...equivalent to the statement that the transfer BC_{p+} \to S^0 admits a section after telescopic localization, which in turn follows from the Kahn-Priddy theorem.
Osteoblastoma is a primary bone-forming tumour that usually occurs in the second decade with an affinity to the posterior elements when found in the spine. Its occurrence in the early first decade is ...uncommon and often causes a diagnostic dilemma. It usually has a late presentation and the symptoms may be non-specific which may lead the clinician to overlook this particular entity. We present a case of osteoblastoma of the posterior elements of the C5 vertebra in a pre-adolescent child who was diagnosed and successfully managed with surgical resection in a timely fashion that led to favourable recovery postoperatively.
We prove a version of faithfully flat descent in rigid analytic geometry, for almost perfect complexes and without finiteness assumptions on the rings involved. This extends results of Drinfeld for ...vector bundles.
We study the étale sheafification of algebraic
K
-theory, called étale
K
-theory. Our main results show that étale
K
-theory is very close to a noncommutative invariant called Selmer
K
-theory, which ...is defined at the level of categories. Consequently, we show that étale
K
-theory has surprisingly well-behaved properties, integrally and without finiteness assumptions. A key theoretical ingredient is the distinction, which we investigate in detail, between sheaves and hypersheaves of spectra on étale sites.
We give an account of the construction of the Bhatt–Morrow–Scholze motivic filtration on topological cyclic homology and related invariants, focusing on the case of equal characteristic p$p$ and the ...connections to crystalline and de Rham–Witt theory.
We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP ...and crystalline-TP spectral sequences need not degenerate.
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