Representation of Original Sense of Chinese Characters by FOPC

PACLIC 20 / Wuhan, China / 1-3 November, 200

Higher theta series for unitary groups over function fields

In previous work, we defined certain virtual fundamental classes for special cycles on the moduli stack of Hermitian shtukas, and related them to the higher derivatives of non-singular Fourier coefficients of Siegel-Eisenstein series. In the present article, we construct virtual fundamental classes in greater generality, including those expected to relate to the higher derivatives of singular Fourier coefficients. We assemble these classes into "higher" theta series, which we conjecture to be modular. Two types of evidence are presented: structural properties affirming that the cycle classes behave as conjectured under certain natural operations such as intersection products, and verification of modularity in several special situations. One innovation underlying these results is a new approach to special cycles in terms of derived algebraic geometry.Comment: Comments welcome

Modularity of higher theta series I: cohomology of the generic fiber

In a previous paper we constructed $\textit{higher}$ theta series for unitary groups over function fields, and conjectured their modularity properties. Here we prove the generic modularity of the $\ell$-adic realization of higher theta series in cohomology. The proof debuts a new type of Fourier transform, occurring on the Borel-Moore homology of moduli spaces for shtuka-type objects, that we call the $\textit{arithmetic Fourier transform}$. Another novelty in the argument is a $\textit{sheaf-cycle correspondence}$ extending the classical sheaf-function correspondence, which facilitates the deployment of sheaf-theoretic methods to analyze algebraic cycles. Although the modularity property is a statement within classical algebraic geometry, the proof relies on derived algebraic geometry, especially a nascent theory of $\textit{derived Fourier analysis}$ on derived vector bundles, which we develop

Higher Siegel--Weil formula for unitary groups: the non-singular terms

We construct special cycles on the moduli stack of unitary shtukas. We prove an identity between (1) the r-th central derivative of non-singular Fourier coefficients of a normalized Siegel--Eisenstein series, and (2) the degree of special cycles of "virtual dimension 0" on the moduli stack of unitary shtukas with r legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein series.Comment: Minor revision

Effect of miR-384-targeting LINC00491 on proliferation, migration and invasion of tongue squamous cell carcinoma cells

Purpose: To investigate the effect of long-chain non-coding RNA LINC00491 (LncRNA LINC00491) on the proliferation, migration and invasion of tongue squamous cell carcinoma (TSCC) cells, and the underlying mechanism. Methods: Real-time quantitative polymerase chain reaction (qRT-PCR) was applied to determine the expressions of LINC00491 and micro-RNA-384 (miR-384). Furthermore, LINC00491 and miR-384 were transfected into CAL-27 cells, while cell cycle was analyzed using flow cytometry. Cell proliferation was determined by methyl thiazolyl diphenyl-tetrazolium (MTT) assay. Cell migration and invasion were evaluated using Transwell experiments. The relationship between LINC00491 and miR-384 was confirmed using double luciferase reporting assay, while protein expression levels of P21, Ki67, E- cadherin, N-cadherin, and vimentin were assayed with Western blotting. Results: The expression of LINC00491 increased in TSCC tissues (p < 0.05). The proportion of cells in G1-phase increased, while the proportion of cells in S-phase decreased (p < 0.05). There was decrease in cell survival, cell migration and cell invasion (p < 0.05). The protein expression levels of Ki67, N- cadherin, and vimentin were lowered, while those of P21, E-cadherin protein were increased (p < 0.05). Transfection of LINC00491 and miR- 384 reduced the proportion of cells in G1 phase, but increased the proportion of cells in S-phase (p < 0.05). Moreover, cell survival, migration and invasion were increased. The protein expressions of Ki67, N-cadherin, and vimentin rose, while those of P21 and E-cadherin decreased (p < 0.05). Conclusion: LINC00491 promotes the proliferation, migration and invasion of TSCC cells by inhibiting miR-384. This finding provides a potential target for the treatment of TSCC