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ALGEBRA & NUMBER THEORY, ISSN 1937-0652, 2018, Volume 12, Issue 7, pp. 1559 - 1580
We give some basics about homological algebra of difference representations. We consider both the difference discrete and the difference rational case. We... 
MATHEMATICS | FIELDS | rational cohomology | DESCENT | difference algebraic group | difference cohomology | Mathematics - Algebraic Geometry
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 12/2019, Volume 22, Issue 6, pp. 1427 - 1455
We verify that universal classes in the cohomology of G L N determine explicit cohomology classes of Frobenius kernels G (r) of various linear algebraic groups... 
Unipotent algebraic groups | Associative Rings and Algebras | 20C20 | Non-associative Rings and Algebras | Commutative Rings and Algebras | 20G05 | Mathematics | Frobenius kernels | Rational cohomology | 20G10 | CO-HOMOLOGY | MATHEMATICS | VARIETIES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 05/2018, Volume 330, pp. 420 - 432
A smooth projective scheme X over a field k is said to satisfy the Rost nilpotence principle if any endomorphism of X in the category of Chow motives that... 
Motivic cohomology | Rost nilpotence | Algebraic cycles | MATHEMATICS | CHOW GROUPS | COEFFICIENTS | K-THEORY | BLOCH-KATO CONJECTURE | RATIONAL SURFACES
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 02/2013, Volume 106, Issue 2, pp. 410 - 444
The Bloch–Beilinson–Murre conjectures predict the existence of a descending filtration on Chow groups of smooth projective varieties which is functorial with... 
MATHEMATICS | ALGEBRAIC CYCLES | CONJECTURES | HYPERSURFACES | RATIONAL EQUIVALENCE | VARIETIES | GENERAL TYPE | MOTIVES | SURFACES | PG=0 | Filtration | Algebra | Mathematical analysis | Ingredients | Topology | Cost engineering | Standards | Incidence | Mathematics - Algebraic Geometry
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2017, Volume 369, Issue 4, pp. 2879 - 2896
Journal Article
Advances in Mathematics, ISSN 0001-8708, 09/2014, Volume 262, pp. 484 - 519
Let G be a connected reductive algebraic group and B be a Borel subgroup defined over an algebraically closed field of characteristic p>0. In this paper, the... 
Rational stability | Cohomology | Algebraic groups | Finite Chevalley groups | ALGEBRAIC-GROUPS | CO-HOMOLOGY | MATHEMATICS | MODULES | LIE TYPE | FROBENIUS KERNELS | 2ND COHOMOLOGY | Computer science
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 01/2018, Volume 18, Issue 1, pp. 247 - 312
Let R be either F-p or a field of characteristic 0. For each R-good topological space Y, we define a collection of higher cohomology operations which, together... 
Toda bracket | Cosimplicial resolution | Higher cohomology operation | MATHEMATICS | HIGHER HOMOTOPY OPERATIONS | RATIONAL HOMOTOPY | CATEGORIES | RESOLUTIONS
Journal Article
Manuscripta Mathematica, ISSN 0025-2611, 11/2013, Volume 142, Issue 3, pp. 409 - 437
In this work we study the additive orbifold cohomology of the moduli stack of smooth genus g curves. We show that this problem reduces to investigating the... 
14H37 | Topological Groups, Lie Groups | 55N32 | 14D23 | Mathematics | 32G15 | Primary: 14H10 | 55P50 | Geometry | Calculus of Variations and Optimal Control; Optimization | Secondary: 14N35 | Mathematics, general | Algebraic Geometry | Number Theory | SPACE | MATHEMATICS | RATIONAL COHOMOLOGY | STACKS | CHEN-RUAN COHOMOLOGY
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 09/2016, Volume 16, Issue 4, pp. 1953 - 2019
For an arbitrary compact Lie group G, we describe a model for rational G-spectra with toral geometric isotropy and show that there is a convergent Adams... 
MATHEMATICS | MODEL | Mathematics - Algebraic Topology
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 01/2018, Volume 18, Issue 1, pp. 187 - 219
A second cohomology class of the group cohomology of the symplectomorphism group is defined for a symplectic manifold with first Chern class proportional to... 
Symplectomorphism group | Simplicial manifold | Characteristic class | MATHEMATICS | HOMOMORPHISMS | 2-COCYCLE | RATIONAL RULED SURFACES | FOLIATED SURFACE BUNDLES | MANIFOLDS | MAPPING CLASS-GROUPS | HOMOLOGY | ORIENTABLE SURFACES
Journal Article
Acta Mathematica, ISSN 0001-5962, 6/2009, Volume 202, Issue 2, pp. 139 - 193
We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental’s heuristic argument, which relates small... 
Mathematics, general | Mathematics | MATHEMATICS | CHEN-RUAN COHOMOLOGY | RING | TORUS ACTIONS | VARIETIES | RATIONAL CURVES | GROMOV-WITTEN INVARIANTS | HOMOLOGY | DELIGNE-MUMFORD STACKS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2009, Volume 222, Issue 3, pp. 729 - 781
We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We... 
Self-similar systems | Random iteration | Fractal geometry | Iterated function systems | Rational semigroups | Cohomology | Complex dynamics | Julia set | JULIA SETS | POLYNOMIALS | MATHEMATICS | MAPS | HYPERBOLIC RATIONAL SEMIGROUPS | DYNAMICS | CONNECTEDNESS | FORM Z+C(N) | RANDOM ITERATIONS
Journal Article
Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2016, Volume 46, Issue 4, pp. 1293 - 1308
We consider zero-cycles on algebraic varieties defined over number fields. The Hasse principle and weak approximation property are obstructed by the Brauer... 
Brauer and Manin's obstruction | Weak approximation | Zero-cycles | Hasse principle | zero-cycles | FIBRATIONS | FIBERED VARIETIES | INTERSECTIONS | MATHEMATICS | weak approximation | BRAUER-MANIN OBSTRUCTION | COHOMOLOGY | CHOW GROUPS | 2 QUADRICS | SPECIALIZATION | RATIONAL SURFACES | SEVERI-BRAUER
Journal Article
Geometry and Topology, ISSN 1465-3060, 01/2014, Volume 18, Issue 1, pp. 291 - 326
We introduce the notion of Q-filtrable varieties: projective varieties with a torus action and a finite number of fixed points, such that the cells of the... 
Algebraic monoids | Algebraic torus actions | GKM theory | Group embeddings | Rational smoothness | Equivariant cohomology | MATHEMATICS | TORUS | FORMALITY | ALGEBRAIC-VARIETIES | K-THEORY | DUALITY | SPECTRUM | MONOIDS | EQUIVARIANT COHOMOLOGY RING | POINTS
Journal Article
2009, 1, Progress in mathematics, ISBN 9780817649333, Volume 282, ix, 310
This volume provides an overview of rationality problems by surveying research from leading experts in the field. Readers will find coverage of rationality... 
Homology theory | Geometry, Algebraic | Mathematics | Rational points (Geometry) | Algebraic Geometry | Group Theory and Generalizations | Topological Groups, Lie Groups
Book
Duke Mathematical Journal, ISSN 0012-7094, 11/2009, Volume 150, Issue 2, pp. 211 - 267
Let X-[n] be the Hilbert scheme of n points on the smooth quasi-projective surface X, and let L-[n] be the tautological bundle on X-[n] naturally associated to... 
MATHEMATICS | MCKAY CORRESPONDENCE | DUALITY | RATIONAL-SINGULARITIES | PROJECTIVE PLANE | SHEAVES | MODULI | CONJECTURE | 14F05 | 20C30 | 14C05 | 18E30
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2016, Volume 282, Issue 3, pp. 1127 - 1136
In this article, we prove that any complex smooth rational surface X which has no automorphism of positive entropy has a finite number of real forms (this is... 
Automorphism groups | 14J26 | 12G05 | Rational surfaces | Real forms | Mathematics, general | 14J50 | 14P05 | Mathematics | Real structures | Galois cohomology | FORMS | MATHEMATICS | PLANE | VARIETIES | ALGEBRAIC-GEOMETRY | Mathematics - Algebraic Geometry
Journal Article
Memoirs of the American Mathematical Society, ISSN 0065-9266, 07/2017, Volume 248, Issue 1176, pp. 1 - 228
Journal Article
Selecta Mathematica, ISSN 1022-1824, 7/2016, Volume 22, Issue 3, pp. 1357 - 1411
We prove a global algebraic version of the Lie–Tresse theorem which states that the algebra of differential invariants of an algebraic pseudogroup action on a... 
53A55 | 58H10 | Pseudogroup action | Algebraic group | Differential syzygy | Mathematics | Spencer cohomology | Rational differential invariant | Tresse derivative | Orbits separation | Invariant derivation | Mathematics, general | 58A20 | 35A30 | MATHEMATICS, APPLIED | INVARIANTS | FINITENESS | PSEUDOGROUPS | CLASSIFICATION | MATHEMATICS | RANK 2 DISTRIBUTIONS | Algebra
Journal Article
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