The Cassels-Tate pairing on polarized Abelian varieties.
The category of cofinite modules for ideals of dimension one and codimension one
The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings
In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding . In this paper we extend this correspondence in a natural way to cover also non-coherent subdivisions. As an application, we show that the Cayley Trick combined with results of Santos on subdivisions...
The centralizer of a classical group and Bruhat-Tits buildings
Let be a unitary group defined over a non-Archimedean local field of odd residue characteristic and let be the centralizer of a semisimple rational Lie algebra element of We prove that the Bruhat-Tits building of can be affinely and -equivariantly embedded in the Bruhat-Tits building of so that the Moy-Prasad filtrations are preserved. The latter property forces uniqueness in the following way. Let and be maps from to which preserve the Moy–Prasad filtrations. We prove that...
The characteristic polynomial of a monodromy transformation attached to a family of curves.
The Chern character for Lie-Rinehart algebras
Let be a commutative -algebra where is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a -connection. Our result generalizes the classical Chern character from the -theory of to the algebraic De Rham cohomology.
The Chern Classes of the Stable Rank 3 Vector Bundles on IP3.
The Chow ring of the stack of cyclic covers of the projective line
In this paper we compute the integral Chow ring of the stack of smooth uniform cyclic covers of the projective line and we give explicit generators.
The Chow rings of smooth complete -embeddings
The Chow-Witt ring.
The class group of a one-dimensional affinoid space
A curve over a non-archimedean valued field is with respect to its analytic structure a finite union of affinoid spaces. The main result states that the class group of a one dimensional, connected, regular affinoid space is trivial if and only if is a subspace of . As a consequence, has locally a trivial class group if and only if the stable reduction of has only rational components.
The classification of 4-dimensional Kähler manifolds with small eigenvalue of the Dirac operator.
The classification of weighted projective spaces
We obtain two classifications of weighted projective spaces: up to hoeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the latter by proving that the Mislin genus of any weighted projective space is rigid.
The Clifford dimension of a projective curve
The closure of a model category
The cohomology of local systems on p-adically uniformized varieties.
The cohomology of Monsky and Washnitzer
The cohomology of p-adic symmetric spaces.
The cohomology of period domains for reductive groups over finite fields
The cohomology ring of polygon spaces
We compute the integer cohomology rings of the “polygon spaces”introduced in [F. Kirwan, Cohomology rings of moduli spaces of vector bundles over Riemann surfaces, J. Amer. Math. Soc., 5 (1992), 853-906] and [M. Kapovich & J. Millson, the symplectic geometry of polygons in Euclidean space, J. of Diff. Geometry, 44 (1996), 479-513]. This is done by embedding them in certain toric varieties; the restriction map on cohomology is surjective and we calculate its kernel using ideas from the theory...