30,597 research outputs found
Twisted Witt Groups of Flag Varieties
Calm\`es and Fasel have shown that the twisted Witt groups of split flag
varieties vanish in a large number of cases. For flag varieties over
algebraically closed fields, we sharpen their result to an if-and-only-if
statement. In particular, we show that the twisted Witt groups vanish in many
previously unknown cases. In the non-zero cases, we find that the twisted total
Witt group forms a free module of rank one over the untwisted total Witt group,
up to a difference in grading.
Our proof relies on an identification of the Witt groups of flag varieties
with the Tate cohomology groups of their K-groups, whereby the verification of
all assertions is eventually reduced to the computation of the (twisted) Tate
cohomology of the representation ring of a parabolic subgroup.Comment: inverse Cartan coefficients for E_7 in Figures 1, 2 and 3 corrected;
related mistake in the marking scheme for diagrams of type E_n corrected;
many minor corrections and clarifications; more example
Singular equivalence and the (Fg) condition
We show that singular equivalences of Morita type with level between
finite-dimensional Gorenstein algebras over a field preserve the (Fg)
condition.Comment: 21 page
Derived invariants of irregular varieties and Hochschild homology
We study the behavior of cohomological support loci of the canonical bundle
under derived equivalence of smooth projective varieties. This is achieved by
investigating the derived invariance of a generalized version of Hochschild
homology. Furthermore, using techniques coming from birational geometry, we
establish the derived invariance of the Albanese dimension for varieties having
non-negative Kodaira dimension. We apply our machinery to study the derived
invariance of the holomorphic Euler characteristic and of certain Hodge numbers
for special classes of varieties. Further applications concern the behavior of
particular types of fibrations under derived equivalence.Comment: Small fixes and substantial expository improvements. 22 page
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