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Laurent F-Crystals and Lubin-Tate (φq, Γ)-Modules- [electronic resource]
![Laurent F-Crystals and Lubin-Tate (φq, Γ)-Modules - [electronic resource]](/Users/Baul/Images/book.png)
Laurent F-Crystals and Lubin-Tate (φq, Γ)-Modules- [electronic resource]
상세정보
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214100459
- ISBN
- 9798379604318
- DDC
- 510
- 저자명
- Marks, Samuel.
- 서명/저자
- Laurent F-Crystals and Lubin-Tate (φq, Γ)-Modules - [electronic resource]
- 발행사항
- [S.l.]: : Harvard University., 2023
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2023
- 형태사항
- 1 online resource(84 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
- 주기사항
- Advisor: Kisin, Mark.
- 학위논문주기
- Thesis (Ph.D.)--Harvard University, 2023.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 요약Let L/ℚp be a finite extension. We introduce L-typical prisms, a mild generalization of prisms. Following ideas of Bhatt, Scholze, and Wu, we show that certain vector bundles, called Laurent F-crystals, on the L-typical prismatic site of a formal scheme X over Spf \uD835\uDCAAL are equivalent to \uD835\uDCAAL-linear local systems on the generic fiber Xη. We also give comparison theorems for computing the etale cohomology of a local system in terms of the cohomology of its corresponding Laurent F-crystal. In the case X = Spf \uD835\uDCAAK for K/L a p-adic field, we show that this recovers the Kisin-Ren equivalence between Lubin-Tate (φq, Γ)-modules and \uD835\uDCAAL-linear representations of GK and the results of Kupferer and Venjakob for computing Galois cohomology in terms of Herr complexes of (φq, Γ)-modules. We can thus regard Laurent F-crystals on the L-typical prismatic site as providing a suitable notion of relative (φq, Γ)-modules.
- 일반주제명
- Mathematics.
- 일반주제명
- Applied mathematics.
- 키워드
- F-crystals
- 키워드
- Vector bundles
- 키워드
- Prismatic site
- 키워드
- Suitable notion
- 기타저자
- Harvard University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 84-12B.
- 기본자료저록
- Dissertation Abstract International
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520240214100459
■006m o d
■007cr#unu||||||||
■020 ▼a9798379604318
■035 ▼a(MiAaPQ)AAI30492666
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aMarks, Samuel.▼0(orcid)0009-0002-3965-4389
■24510▼aLaurent F-Crystals and Lubin-Tate (φq, Γ)-Modules▼h[electronic resource]
■260 ▼a[S.l.]:▼bHarvard University. ▼c2023
■260 1▼aAnn Arbor :▼bProQuest Dissertations & Theses, ▼c2023
■300 ▼a1 online resource(84 p.)
■500 ▼aSource: Dissertations Abstracts International, Volume: 84-12, Section: B.
■500 ▼aAdvisor: Kisin, Mark.
■5021 ▼aThesis (Ph.D.)--Harvard University, 2023.
■506 ▼aThis item must not be sold to any third party vendors.
■520 ▼aLet L/ℚp be a finite extension. We introduce L-typical prisms, a mild generalization of prisms. Following ideas of Bhatt, Scholze, and Wu, we show that certain vector bundles, called Laurent F-crystals, on the L-typical prismatic site of a formal scheme X over Spf \uD835\uDCAAL are equivalent to \uD835\uDCAAL-linear local systems on the generic fiber Xη. We also give comparison theorems for computing the etale cohomology of a local system in terms of the cohomology of its corresponding Laurent F-crystal. In the case X = Spf \uD835\uDCAAK for K/L a p-adic field, we show that this recovers the Kisin-Ren equivalence between Lubin-Tate (φq, Γ)-modules and \uD835\uDCAAL-linear representations of GK and the results of Kupferer and Venjakob for computing Galois cohomology in terms of Herr complexes of (φq, Γ)-modules. We can thus regard Laurent F-crystals on the L-typical prismatic site as providing a suitable notion of relative (φq, Γ)-modules.
■590 ▼aSchool code: 0084.
■650 4▼aMathematics.
■650 4▼aApplied mathematics.
■653 ▼aPrismatic cohomology
■653 ▼aF-crystals
■653 ▼aVector bundles
■653 ▼aPrismatic site
■653 ▼aSuitable notion
■690 ▼a0405
■690 ▼a0364
■71020▼aHarvard University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g84-12B.
■773 ▼tDissertation Abstract International
■790 ▼a0084
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T16932444▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
■980 ▼a202402▼f2024
