(05/01 ~ 05/01)
조성윤 님의
404호 예약입니다.
조성윤
2025-03-20
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성명
조성윤
호실
404호
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날짜
20250501 ~ 20250501시간
16:00 ~ 18:00 -
연락처
이메일
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인원수
20
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세미나
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내용
<POSTECH PMI Number Theory Seminar>
Title: Degenerations of D-shtukas over ramified legs
Abstract: The canonical integral models of Shimura varieties associated with reductive groups that are anisotropic modulo center are expected to be proper. However, an analogous property is known to be false for the moduli stack of shtukas over global function fields. More precisely, given a proper smooth curve X over a finite field and a parahoric group scheme G over X corresponding to a maximal order of a central division algebra D over the function field of X, Eike Lau obtained a numerical criterion for the properness of the moduli stack of bounded G-shtukas with legs in the split locus of D. As a consequence, there exists an instance where the moduli stack of bounded G-shtukas is not proper over the split locus of D.
Based on the work of Arasteh Rad—Hartl and Bieker, the moduli stack of bounded G-shtukas is allowed to have legs in the ramification locus of D. We extend Lau's result to the case where the legs are allowed to lie in the ramification locus, showing in particular that the moduli stack of G-shtukas can be proper when the legs are restricted to the split locus of D, but not proper when the legs run over the whole curve. This is joint work with Wansu Kim and Junyeong Park.
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