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    Local P-shtukas and their relation to global G-shtukas

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    This is the first in a sequence of two articles investigating moduli stacks of global G-shtukas, which are function field analogs for Shimura varieties. Here G is a flat affine group scheme of finite type over a smooth projective curve, and global G-shtukas are generalizations of Drinfeld shtukas and analogs of abelian varieties with additional structure. Our moduli stacks generalize various moduli spaces used by different authors to prove instances of the Langlands program over function fields. In the present article we explain the relation between global G-shtukas and local P-shtukas, which are the function field analogs of p-divisible groups with additional structure. We prove the analog of a theorem of Serre and Tate stating the equivalence between the deformations of a global G-shtuka and its associated local P-shtukas. We also investigate local P-shtukas alone and explain their relation with Galois representations through their Tate modules. And if P is a smooth affine group scheme with connected reductive generic fiber we prove the existence of Rapoport--Zink spaces for bounded local P-shtukas as formal schemes locally formally of finite type. In the sequel to this article we use these Rapoport--Zink spaces to uniformize the moduli stacks of global G-shtukas.Comment: 37 pages, v3: generalization to flat affine group schemes of finite type, v3: final version which appears in Muenster J. of Mathematic

    Does Lecture Capturing Impact Student Performance and Attendance in an Introductory Accounting Course?

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    The study empirically examines the interplay between lecture capturing viewership, performance and attendance for students in the Middle Eastern country of Qatar. The sample consists of 254 students enrolled in an introductory accounting class either in the Fall semester or in the Spring semester. We show a weak positive relationship between lecture capturing and performance, especially in the presence of other variables such as GPA, attendance, gender and seniority. However, we do not find that lecture capturing reduces attendance. Actual performance results are contrasted with students' perception of the usefulness and effectiveness of lecture capturing. Survey responses reveal that, overall, students attribute a great deal of credit to this pedagogical resource. They stated that lecture capturing clarifies concepts discussed in class, assists in studying for exams, enhances exam results and increases interest in the course. However, the majority of low-performing students believe lecture capturing to be a substitute for attending traditional lectures.Scopu
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