scholarly journals ON THE IRREDUCIBLE COMPONENTS OF SOME CRYSTALLINE DEFORMATION RINGS

2020 ◽  
Vol 8 ◽  
Author(s):  
ROBIN BARTLETT
Keyword(s):  
Moduli Space ◽  
Finite Extension ◽  
Crystalline Representations ◽  
Irreducible Components ◽  
Deformation Rings ◽  
Deformation Ring

We adapt a technique of Kisin to construct and study crystalline deformation rings of $G_{K}$ for a finite extension $K/\mathbb{Q}_{p}$ . This is done by considering a moduli space of Breuil–Kisin modules, satisfying an additional Galois condition, over the unrestricted deformation ring. For $K$ unramified over $\mathbb{Q}_{p}$ and Hodge–Tate weights in $[0,p]$ , we study the geometry of this space. As a consequence, we prove that, under a mild cyclotomic-freeness assumption, all crystalline representations of an unramified extension of  $\mathbb{Q}_{p}$ , with Hodge–Tate weights in $[0,p]$ , are potentially diagonalizable.

scholarly journals Moduli of Space Sheaves with Hilbert Polynomial 4m+ 1

2018 ◽  
Vol 61 (2) ◽  
pp. 328-345 ◽  
Author(s):  
Mario Maican
Keyword(s):  
Euler Characteristic ◽  
Moduli Space ◽  
Elementary Proof ◽  
Hilbert Polynomial ◽  
Space Curves ◽  
Irreducible Components

AbstractWe investigate the moduli space of sheaves supported on space curves of degree and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of three irreducible components.

scholarly journals The irreducible components of the moduli space of dihedral covers of algebraic curves

2015 ◽  
Vol 9 (4) ◽  
pp. 1185-1229 ◽  
Author(s):  
Fabrizio Catanese ◽  
Michael Lönne ◽  
Fabio Perroni
Keyword(s):  
Moduli Space ◽  
Algebraic Curves ◽  
Irreducible Components

scholarly journals The Supersingular Locus of the Shimura Variety for GU(1, s)

2010 ◽  
Vol 62 (3) ◽  
pp. 668-720 ◽  
Author(s):  
Inken Vollaard
Keyword(s):  
Complete Intersection ◽  
Moduli Space ◽  
Unitary Group ◽  
Shimura Variety ◽  
Incidence Relation ◽  
Irreducible Components ◽  
Reduction Modulo ◽  
Tits Building ◽  
Divisible Groups ◽  
Dieudonne Theory

AbstractIn this paper we study the supersingular locus of the reduction modulopof the Shimura variety for GU(1,s) in the case of an inert primep. Using Dieudonné theory we define a stratification of the corresponding moduli space ofp-divisible groups. We describe the incidence relation of this stratification in terms of the Bruhat–Tits building of a unitary group.In the case of GU(1, 2), we show that the supersingular locus is equidimensional of dimension 1 and is of complete intersection. We give an explicit description of the irreducible components and their intersection behaviour.

scholarly journals ON THE MONODROMY AND GALOIS GROUP OF CONICS LYING ON HEISENBERG INVARIANT QUARTIC K3 SURFACES

2019 ◽  
Vol 62 (3) ◽  
pp. 640-660
Author(s):  
FLORIAN BOUYER
Keyword(s):  
Galois Group ◽  
Moduli Space ◽  
Monodromy Group ◽  
K3 Surfaces ◽  
K3 Surface ◽  
Field Of Definition ◽  
Irreducible Components ◽  
Definition Of

AbstractIn [5], Eklund showed that a general (ℤ/2ℤ)4 -invariant quartic K3 surface contains at least 320 conics. In this paper, we analyse the field of definition of those conics as well as their Monodromy group. As a result, we prove that the moduli space of (ℤ/2ℤ)4-invariant quartic K3 surface with a certain marked conic has 10 irreducible components.

scholarly journals RATIONAL FAMILIES OF VECTOR BUNDLES ON CURVES

2004 ◽  
Vol 15 (01) ◽  
pp. 13-45 ◽  
Author(s):  
ANA-MARIA CASTRAVET
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Rational Curves ◽  
Complex Curve ◽  
Stable Vector Bundles ◽  
Irreducible Components ◽  
Rationally Connected ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

Let C be a smooth projective complex curve of genus g≥2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k≥1, we find all the irreducible components of the space of rational curves on M, of degree k. In particular, we find the maximal rationally connected fibrations of these components. We prove that there is a one-to-one correspondence between moduli spaces of rational curves on M and moduli spaces of rank 2 vector bundles on ℙ1×C.

scholarly journals Deformation Theory of the Trivial mod p Galois Representation for GLn

2020 ◽  
Author(s):  
Ashwin Iyengar
Keyword(s):  
Deformation Theory ◽  
Finite Extension ◽  
Galois Representation ◽  
Deformation Space ◽  
Absolute Galois Group ◽  
Trivial Representation ◽  
Characteristic P ◽  
Generic Fiber ◽  
Mild Conditions ◽  
Irreducible Components

Abstract We study the rigid generic fiber $\mathcal{X}^\square _{\overline \rho }$ of the framed deformation space of the trivial representation $\overline \rho : G_K \to \textrm{GL}_n(k)$ where $k$ is a finite field of characteristic $p>0$ and $G_K$ is the absolute Galois group of a finite extension $K/\textbf{Q}_p$. Under some mild conditions on $K$ we prove that $\mathcal{X}^\square _{\overline \rho }$ is normal. When $p> n$ we describe its irreducible components and show Zariski density of its crystalline points.

scholarly journals Surfaces with pg = q = 2, K2 = 6, and Albanese Map of Degree 2

2013 ◽  
Vol 65 (1) ◽  
pp. 195-221 ◽  
Author(s):  
Matteo Penegini ◽  
Francesco Polizzi
Keyword(s):  
Moduli Space ◽  
Minimal Surfaces ◽  
General Type ◽  
Disjoint Union ◽  
Double Cover ◽  
Surfaces Of General Type ◽  
Irreducible Components ◽  
Albanese Map

AbstractWe classify minimal surfaces of general type with pg = q = 2 and K2 = 6 whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth irreducible components MIa, MIb, MII of dimension 4, 4, 3, respectively.

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