共查询到20条相似文献,搜索用时 15 毫秒
1.
Olivier Penacchio 《Comptes Rendus Mathematique》2002,335(5):475-480
Let X be a smooth projective variety over an algebraically closed field of characteristic 0. We prove that the category of μ-semistable reflexive sheaves of slope μ equivariant for the action of some group on X is Abelian. The same claim for and a stronger semistability condition gives us a geometric proof of the fact that the category of mixed Hodge structures is Abelian. To cite this article: O. Penacchio, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 475–480. 相似文献
2.
Reuben Rabi 《manuscripta mathematica》2001,105(4):425-469
We construct certain extensions of Hodge structures using points on algebraic curves and study them. We also introduce and
use a related function theory which forms a genus g > 0 version of that of classical hyperlogarithms.
Received: 9 May 2000 / Revised version: 8 December 2000 相似文献
3.
Doosung Park 《Journal of Pure and Applied Algebra》2019,223(10):4123-4152
We construct the equivariant version of cd-structures, and we develop descent theory for topologies coming from equivariant cd-structures. In particular, we reprove several results of Cisinski–Déglies on étale descent, qfh-descent, and h-descent. Since the étale topos, qfh-topos, and h-topos do not come from usual cd-structures, such results cannot be produced by usual cd-structures. We also apply equivariant cd-structures to study several topologies on the category of noetherian fs log schemes. 相似文献
4.
Yannick Henrio 《manuscripta mathematica》2001,106(2):131-150
Let R be a complete discrete valuation ring of mixed characteristics, with algebraically closed residue field k. We study the existence problem of equivariant liftings to R of Galois covers of nodal curves over k. Using formal geometry, we show that this problem is actually a local one. We apply this local-to-global principle to obtain
new results concerning the existence of such liftings.
Received: 10 February 2000 / Revised version: 13 September 2000 相似文献
5.
6.
We consider arithmetic varieties endowed with an action of the group scheme of n-th roots of unity and we define equivariant arithmetic K
0-theory for these varieties. We use the equivariant analytic torsion to define direct image maps in this context and we prove
a Riemann-Roch theorem for the natural transformation of equivariant arithmetic K
0-theory induced by the restriction to the fixed point scheme; this theorem can be viewed as an analog, in the context of Arakelov
geometry, of the regular case of the theorem proved by P. Baum, W. Fulton and G. Quart in [BaFQ]. We show that it implies
an equivariant refinement of the arithmetic Riemann-Roch theorem, in a form conjectured by J.-M. Bismut (cf. [B2, Par. (l),
p. 353] and also Ch. Soulé’s question in [SABK, 1.5, p. 162]).
Oblatum 22-I-1999 & 20-II-2001?Published online: 4 May 2001 相似文献
7.
We prove a formula expressing the motivic integral (Loeser and Sebag, 2003) [34] of a K3 surface over C((t)) with semi-stable reduction in terms of the associated limit mixed Hodge structure. Secondly, for every smooth variety over a complete discrete valuation field we define an analogue of the monodromy pairing, constructed by Grothendieck in the case of abelian varieties, and prove that our monodromy pairing is a birational invariant of the variety. Finally, we propose a conjectural formula for the motivic integral of maximally degenerate K3 surfaces over an arbitrary complete discrete valuation field and prove this conjecture for Kummer K3 surfaces. 相似文献
8.
Alice Garbagnati 《manuscripta mathematica》2013,140(3-4):273-294
The aim of this paper is to construct families of Calabi-Yau threefolds without boundary points with maximal unipotent monodromy and to describe the variation of their Hodge structures. In particular five families are constructed. In all these cases the variation of the Hodge structures of the Calabi-Yau threefolds is basically the variation of the Hodge structures of a family of curves. This allows us to write explicitly the Picard-Fuchs equation for the one-dimensional families. These Calabi-Yau threefolds are desingularizations of quotients of the product of a (fixed) elliptic curve and a K3 surface admitting an automorphisms of order 4 (with some particular properties). We show that these K3 surfaces admit an isotrivial elliptic fibration. 相似文献
9.
Kenichi Bannai 《Mathematische Zeitschrift》2002,242(3):443-480
The purpose of this paper is to interpret rigid syntomic cohomology, defined by Amnon Besser [Bes], as a p-adic absolute Hodge cohomology. This is a p-adic analogue of a work of Beilinson [Be1] which interprets Beilinson-Deligne cohomology in terms of absolute Hodge cohomology.
In the process, we will define a theory of p-adic absolute Hodge cohomology with coefficients, which may be interpreted as a generalization of rigid syntomic cohomology
to the case with coefficients.
Received: 25 September 2000 / In final form: 23 March 2001 / Published online: 28 February 2002 相似文献
10.
Gregory J. Pearlstein 《manuscripta mathematica》2000,102(3):269-310
Following C. Simpson, we show that every variation of graded-polarized mixed Hodge structure defined over ℚ carries a natural
Higgs bundle structure which is invariant under the ℂ* action studied in [20]. We then specialize our construction to the context of [6], and show that the resulting Higgs field
θ determines (and is determined by) the Gromov–Witten potential of the underlying family of Calabi–Yau threefolds.
Received: 14 February 2000 相似文献
11.
《Mathematische Nachrichten》2017,290(17-18):2800-2814
A classical example of Mumford gives a generically non‐reduced component of the Hilbert scheme of smooth curves in such that a general element of the component is contained in a smooth cubic surface in . In this article we use techniques from Hodge theory to give further examples of such (generically non‐reduced) components of Hilbert schemes of smooth curves without any restriction on the degree of the surface containing it. As a byproduct we also obtain generically non‐reduced components of certain Hodge loci. 相似文献
12.
Laura Scull 《Transactions of the American Mathematical Society》2008,360(5):2505-2525
In the equivariant category of spaces with an action of a finite group, algebraic `minimal models' exist which describe the rational homotopy for -spaces which are 1-connected and of finite type. These models are diagrams of commutative differential graded algebras. In this paper we prove that a model category structure exists on this diagram category in such a way that the equivariant minimal models are cofibrant objects. We show that with this model structure, there is a Quillen equivalence between the equivariant category of rational -spaces satisfying the above conditions and the algebraic category of the models.
13.
Jörg Wildeshaus 《Comptes Rendus Mathematique》2003,337(7):467-472
We study algebraic mixed Hodge modules on the (relative) affine space which are of normal crossing type. Our main result (Theorem 4.3) gives an equivalence between the category of Hodge modules of normal crossing type, and the category of hypercubes of admissible variations on S. If the base S is a point, then 4.3 is the Hodge theoretic analogue of the main result of Galligo et al. (Ann. Inst. Fourier 35 (1985) 1–48). To cite this article: J. Wildeshaus, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
14.
We conjecture that derived categories of coherent sheaves on fake projective n -spaces have a semi-orthogonal decomposition into a collection of n+1 exceptional objects and a category with vanishing Hochschild homology. We prove this for fake projective planes with non-abelian automorphism group (such as Keum's surface). Then by passing to equivariant categories we construct new examples of phantom categories with both Hochschild homology and Grothendieck group vanishing. 相似文献
15.
Volodymyr Lyubashenko 《Applied Categorical Structures》2002,10(4):331-381
We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal. 相似文献
16.
We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic
tori, in terms of structure of the zero- and one-dimensional orbits. The class of varieties to which our formula applies includes
Schubert varieties in flag varieties and affine flag varieties. We also prove a monotonicity result on local intersection
cohomology stalks.
Received: 9 November 2000 / Published online: 24 September 2001 相似文献
17.
Kōta Yoshioka 《Mathematische Annalen》2001,321(4):817-884
In this paper, we consider basic problems on moduli spaces of stable sheaves on abelian surfaces. Our main assumption is
the primitivity of the associated Mukai vector. We determine the deformation types, albanese maps, Bogomolov factors and their
weight 2 Hodge structures. We also discuss the deformation types of moduli spaces of stable sheaves on K3 surfaces.
Received: 28 February 2000 / Revised version: 15 September 2000 / Published online: 24 September 2001 相似文献
18.
Vladimir Hinich 《Advances in Mathematics》2005,195(1):102-164
19.
J. Nagel 《Mathematische Annalen》1998,312(2):387-401
We verify the generalized Hodge conjecture GHC(X,5,2) for the quadratic complex of lines in projective four–space.
Received: 27 February 1998 / Revised version: 13 May 1998 相似文献
20.
R.N. Karasev 《Topology and its Applications》2009,156(14):2406-2415
In this paper configuration spaces of smooth manifolds are considered. The accent is made on actions of certain groups (mostly p-tori) on this spaces by permuting their points. For such spaces the cohomological index, the genus in the sense of Krasnosel'skii-Schwarz, and the equivariant Lyusternik-Schnirelmann category are estimated from below, and some corollaries for functions on configuration spaces are deduced. 相似文献