Abstract
We develop techniques of mimicking the Frobenius action in the study of universal homeomorphisms in mixed characteristic. As a consequence, we show a mixed characteristic Keel’s base point free theorem obtaining applications towards the mixed characteristic Minimal Model Program, we generalise Kollár’s theorem on the existence of quotients by finite equivalence relations to mixed characteristic, and we provide a new proof of the existence of quotients by affine group schemes.
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@MISC{aemw,
author = {Achinger, P. and Elmanto, E. and Mathew, A. and Witaszek, J.},
title = {K-theory and universal homeomorphisms in mixed characteristic},
note = {private communication},
zblnumber = {},
} -
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author = {André,
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title = {La conjecture du facteur direct},
journal = {Publ. Math. Inst. Hautes \'{E}tudes Sci.},
fjournal = {Publications Mathématiques. Institut de Hautes \'{E}tudes Scientifiques},
volume = {127},
year = {2018},
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mrclass = {13D22 (13A35 13B40 13D09 18A99)},
mrnumber = {3814651},
mrreviewer = {Marcel Morales},
doi = {10.1007/s10240-017-0097-9},
url = {https://doi.org/10.1007/s10240-017-0097-9},
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} -
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url = {https://doi.org/10.2307/1970602},
zblnumber = {0177.49003},
} -
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@MISC{BS19,
author = {Bhatt, Bhargav and Scholze, P.},
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arxiv = {1905.08229},
zblnumber = {},
} -
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author = {Bhatt, Bhargav},
title = {On the direct summand conjecture and its derived variant},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {212},
year = {2018},
number = {2},
pages = {297--317},
issn = {0020-9910},
mrclass = {13D22 (13D09)},
mrnumber = {3787829},
mrreviewer = {Linquan Ma},
doi = {10.1007/s00222-017-0768-7},
url = {https://doi.org/10.1007/s00222-017-0768-7},
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author = {Bhatt, Bhargav and Scholze, Peter},
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mrclass = {14F05 (14M15 19G12)},
mrnumber = {3674218},
mrreviewer = {Marc-Hubert Nicole},
doi = {10.1007/s00222-016-0710-4},
url = {https://doi.org/10.1007/s00222-016-0710-4},
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mrnumber = {4100119},
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url = {https://doi.org/10.1112/plms.12323},
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title = {Classification of Higher Dimensional Algebraic Varieties},
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author = {Keel, Se\'{a}n},
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author = {Keeler, Dennis S.},
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title = {Birational Geometry of Algebraic Varieties},
series = {Cambridge Tracts in Math.},
volume = {134},
note = {with the collaboration of C. H. Clemens and A. Corti,; translated from the 1998 Japanese original},
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journal = {Ann. of Math. (2)},
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volume = {145},
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@INCOLLECTION{kollar12,
author = {Koll\'{a}r, J\'{a}nos},
title = {Quotients by finite equivalence relations},
booktitle = {Current Developments in Algebraic Geometry},
series = {Math. Sci. Res. Inst. Publ.},
volume = {59},
pages = {227--256},
note = {with an appendix by Claudiu Raicu},
publisher = {Cambridge Univ. Press, Cambridge},
year = {2012},
mrclass = {14A15 (14E20)},
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note = {With a collaboration of S\'{a}ndor Kov\'{a}cs},
publisher = {Cambridge Univ. Press, Cambridge},
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isbn = {978-1-107-03534-8},
mrclass = {14E30 (14B05)},
mrnumber = {3057950},
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doi = {10.1017/CBO9781139547895},
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note={\emph{J. Algebraic Geom.},
to appear},
year = {2019},
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