Hilbert-Samuel polynomials of a proper morphism

1978 ◽  
Vol 158 (2) ◽  
pp. 107-124 ◽  
Author(s):  
Constantin Bănică ◽  
Vasile Brînzănescu
Keyword(s):  
Proper Morphism

scholarly journals -DIVISIBILITY FOR COHERENT COHOMOLOGY

2015 ◽  
Vol 3 ◽  
Author(s):  
BHARGAV BHATT
Keyword(s):  
Hodge Theory ◽  
Mixed Characteristic ◽  
Rational Singularities ◽  
Proper Morphism

We prove that the coherent cohomology of a proper morphism of noetherian schemes can be made arbitrarily$p$-divisible by passage to proper covers (for a fixed prime$p$). Under some extra conditions, we also show that$p$-torsion can be killed by passage to proper covers. These results are motivated by the desire to understand rational singularities in mixed characteristic, and have applications in$p$-adic Hodge theory.

scholarly journals Moduli of complexes on a proper morphism

2006 ◽  
Vol 15 (1) ◽  
pp. 175-206 ◽  
Author(s):  
Max Lieblich
Keyword(s):  
Proper Morphism

The arithmetic plurigenera of surfaces

1979 ◽  
Vol 85 (1) ◽  
pp. 25-31
Author(s):  
P. M. H. Wilson
Keyword(s):  
Smooth Surface ◽  
Projective Surface ◽  
Complex Projective Surface ◽  
Proper Morphism ◽  
The Family ◽  
Complex Projective ◽  
Positive Integers ◽  
Smooth Deformation

Let S0 be a complex projective surface with only isolated Gorenstein singularities (see Introduction to (12)). By Serre's criterion ((4), p. 185) this is equivalent to saying that S0 is normal and Gorenstein. By an algebraic smooth deformation of S0, we shall mean a flat, proper morphism of varieties, ρ: say, with fibre ρ−1(y0) = S0 for some y0 ∈ Y and with the general fibre ρ−1(y) = S being a smooth surface. In the paper (12), we studied such smooth deformations of S0 and in particular the behaviour of the plurigenera Pn of the surfaces in the family. The main result of (12) was the fact that Pn(S0) ≤ Pn(S) for all positive integers n, where the choice of the particular smooth surface was irrelevant by a result of Iitaka(5). To prove the above result we introduced what were called the arithmetic plurigenera of S0, which we define again below. In this paper we shall study more closely these arithmetic quantities, and in the process answer some of the questions posed in (11).

scholarly journals On higher direct images of convergent isocrystals

2019 ◽  
Vol 155 (11) ◽  
pp. 2180-2213
Author(s):  
Daxin Xu
Keyword(s):  
Comparison Theorem ◽  
Direct Image ◽  
Perfect Field ◽  
Frobenius Morphism ◽  
Witt Vectors ◽  
Proper Morphism ◽  
De Rham

Let $k$ be a perfect field of characteristic $p>0$ and let $\operatorname{W}$ be the ring of Witt vectors of $k$. In this article, we give a new proof of the Frobenius descent for convergent isocrystals on a variety over $k$ relative to $\operatorname{W}$. This proof allows us to deduce an analogue of the de Rham complexes comparison theorem of Berthelot [$\mathscr{D}$-modules arithmétiques. II. Descente par Frobenius, Mém. Soc. Math. Fr. (N.S.) 81 (2000)] without assuming a lifting of the Frobenius morphism. As an application, we prove a version of Berthelot’s conjecture on the preservation of convergent isocrystals under the higher direct image by a smooth proper morphism of $k$-varieties.

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