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• W3048051308 endingPage "1175" @default.
• W3048051308 startingPage "1111" @default.
• W3048051308 abstract "This is a modest attempt to study, in a systematic manner, the structure of low dimensional varieties in positive characteristics using $p$-adic invariants. The main objects of interest in this paper are surfaces and threefolds. It is known that there are many (counter) examples of `pathological' or unexpected behavior in surfaces and even of threefolds. Our focus has been on, obtaining systematically, general positive results instead of counter examples. There are many results we prove in this paper and not all can be listed in this abstract. Here are some of the results we prove: We show that $c_1^2leq 5c_2+6b_1$ holds for a large class of surfaces (of general type). We prove that for a smooth, projective, Hodge-Witt, minimal surface of general type (with additional assumptions such as slopes of Frobenius on $H^2_{cris}(X)$ are $geqfrac{1}{2}$) that $$c_1^2leq 5c_2.$$ Novelty of our method lies in our use of slopes of Frobenius (and Hodge-Witt assumption which allows us to control the slope spectral sequence). We also construct new birational invariants of surfaces. Applying our methods to threefolds, we characterise Calabi-Yau threefolds with $b_3=0$." @default.
• W3048051308 created "2020-08-13" @default.
• W3048051308 creator A5036643969 @default.
• W3048051308 date "2020-08-06" @default.
• W3048051308 modified "2023-10-16" @default.
• W3048051308 title "Crystalline aspects of geography of low dimensional varieties I: numerology" @default.
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• W3048051308 doi "https://doi.org/10.1007/s40879-020-00416-x" @default.
• W3048051308 hasPublicationYear "2020" @default.
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