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We define the Chow t-structure on the ∞-category of motivic spectra SH(k) over an arbitrary base field k. We identify the heart of this t-structure SH(k)c♡ when the exponential characteristic of k is inverted. Restricting to the cellular subcategory, we identify the Chow heart SH(k)cell,c♡ as the category of even graded MU2∗MU-comodules. Furthermore, we show that the ∞-category of modules over the Chow truncated sphere spectrum 1c=0 is algebraic. Our results generalize the ones in Gheorghe–Wang–Xu in three aspects: to integral results; to all base fields other than just C; to the entire ∞-category of motivic spectra SH(k), rather than a subcategory containing only certain cellular objects. We also discuss a strategy for computing motivic stable homotopy groups of (p-completed) spheres over an arbitrary base field k using the Postnikov–Whitehead tower associated to the Chow t-structure and the motivic Adams spectral sequences over k.
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Monolithic Integration of Si3N4 Ring Resonator and On-Chip Fourier Transform Spectrometer for The Lab-On-A-Chip Biosensor
We demonstrated the monolithically integrated biosensor with micro-ring-resonator (MRR) and spatial-heterodyne Fourier-transform-spectrometer (SH-FTS) on Si3N4-on-SiO2, substituting the external optical spectrum analyzer. The spectrum is retrieved from SH-FTS with the bulk sensitivity of 42.9 nm/RIU.
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- Award ID(s):
- 1932753
- PAR ID:
- 10346766
- Editor(s):
- Jiang, Wei; Alan Wang
- Date Published:
- Journal Name:
- Cleo
- ISSN:
- 0928-9062
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/N/A
