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1. The eigensplitting of the fiber of the cyclotomic trace for the sphere spectrum

   https://doi.org/10.1090/tran/8822  

   Blumberg, Andrew; Mandell, Michael (January 2022, Transactions of the American Mathematical Society)

   Let p ∈ Z p\in {\mathbb {Z}} be an odd prime. We show that the fiber sequence for the cyclotomic trace of the sphere spectrum S {\mathbb {S}} admits an “eigensplitting” that generalizes known splittings on K K -theory and T C TC . We identify the summands in the fiber as the covers of Z p {\mathbb {Z}}_{p} -Anderson duals of summands in the K ( 1 ) K(1) -localized algebraic K K -theory of Z {\mathbb {Z}} . Analogous results hold for the ring Z {\mathbb {Z}} where we prove that the K ( 1 ) K(1) -localized fiber sequence is self-dual for Z p {\mathbb {Z}}_{p} -Anderson duality, with the duality permuting the summands by i ↦ p − i i\mapsto p-i (indexed mod p − 1 p-1 ). We explain an intrinsic characterization of the summand we call Z Z in the splitting T C ( Z ) p ∧ ≃ j ∨ Σ j ′ ∨ Z TC({\mathbb {Z}})^{\wedge }_{p}\simeq j \vee \Sigma j’\vee Z in terms of units in the p p -cyclotomic tower of Q p {\mathbb {Q}}_{p} . 

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2. THE BOUNDARY OF THE p -RANK STRATUM OF THE MODULI SPACE OF CYCLIC COVERS OF THE PROJECTIVE LINE

   https://doi.org/10.1017/nmj.2022.12  

   OZMAN, EKIN; PRIES, RACHEL; WEIR, COLIN (December 2022, Nagoya Mathematical Journal)

   Abstract. We study the p-rank stratification of the moduli space of cyclic degree ! covers of the projective line in characteristic p for distinct primes p and !. The main result is about the intersection of the p-rank 0 stratum with the boundary of the moduli space of curves. When ! = 3 and p ≡ 2 mod 3 is an odd prime, we prove that there exists a smooth trielliptic curve in characteristic p, for every genus g, signature type (r,s), and p-rank f satisfying the clear necessary conditions. 

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3. Mapping the uneven geographies of digital phenomena: The case of blockchain

   https://doi.org/10.1111/cag.12738  

   Zook, Matthew; McCanless, Michael (December 2021, Canadian Geographies / Géographies canadiennes)

   Key messages Grounding practices within the materiality of geography is an important technique for studying the complexity of digital phenomena.The DIGO (Discourses, Infrastructures, Groupings, and Outcomes) framework uses these categories to guide data selection for locating digital phenomenon in material geographies.This article applies the DIGO framework to blockchain (using data about tweets, miners, firms, and ICOs) to show how this digital practice connects to and across material geographies. 

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4. The Importance of Archiving the Seafloor

   https://doi.org/10.1029/2024EO240020  

   DiCenzo, Christina; Kelley, Katherine A; Anest, Nichole; Fritz, Cara; Donnelly, Jeff (January 2024, Eos)

   Marine geological sample repositories are vital for ocean science, climate change studies, and more. The value of their collections is growing amid efforts to meet rising demand for their services. 

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5. The application of metacommunity theory to the management of riverine ecosystems

   https://doi.org/10.1002/wat2.1557  

   Patrick, Christopher J.; Anderson, Kurt E.; Brown, Brown L.; Hawkins, Charles P.; Metcalfe, Anya; Saffarinia, Parsa; Siqueira, Tadeu; Swan, Christopher M.; Tonkin, Jonathan D.; Yuan, Lester L. (September 2021, WIREs Water)

   Abstract River managers strive to use the best available science to sustain biodiversity and ecosystem function. To achieve this goal requires consideration of processes at different scales. Metacommunity theory describes how multiple species from different communities potentially interact with local‐scale environmental drivers to influence population dynamics and community structure. However, this body of knowledge has only rarely been used to inform management practices for river ecosystems. In this article, we present a conceptual model outlining how the metacommunity processes of local niche sorting and dispersal can influence the outcomes of management interventions and provide a series of specific recommendations for applying these ideas as well as research needs. In all cases, we identify situations where traditional approaches to riverine management could be enhanced by incorporating an understanding of metacommunity dynamics. A common theme is developing guidelines for assessing the metacommunity context of a site or region, evaluating how that context may affect the desired outcome, and incorporating that understanding into the planning process and methods used. To maximize the effectiveness of management activities, scientists, and resource managers should update the toolbox of approaches to riverine management to reflect theoretical advances in metacommunity ecology. This article is categorized under:Water and Life > Nature of Freshwater EcosystemsWater and Life > Conservation, Management, and AwarenessWater and Life > Methods 

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