17,601 research outputs found
A going down theorem for Grothendieck Chow motives
Let X be a geometrically split, geometrically irreducible variety over a
field F satisfying Rost nilpotence principle. Consider a field extension E/F
and a finite field K. We provide in this note a motivic tool giving sufficient
conditions for so-called outer motives of direct summands of the Chow motive of
X_E with coefficients in K to be lifted to the base field. This going down
result has been used S. Garibaldi, V. Petrov and N. Semenov to give a complete
classification of the motivic decompositions of projective homogeneous
varieties of inner type E_6 and to answer a conjecture of Rost and Springer.Comment: Final version of the manuscrip
Classification of upper motives of algebraic groups of inner type A_n
Let A, A' be two central simple algebras over a field F and \mathbb{F} be a
finite field of characteristic p. We prove that the upper indecomposable direct
summands of the motives of two anisotropic varieties of flags of right ideals
X(d_1,...,d_k;A) and X(d'_1,...,d'_s;A') with coefficients in \mathbb{F} are
isomorphic if and only if the p-adic valuations of gcd(d_1,...,d_k) and
gcd(d'_1,..,d'_s) are equal and the classes of the p-primary components A_p and
A'_p of A and A' generate the same group in the Brauer group of F. This result
leads to a surprising dichotomy between upper motives of absolutely simple
adjoint algebraic groups of inner type A_
Motivic decompositions of projective homogeneous varieties and change of coefficients
We prove that under some assumptions on an algebraic group ,
indecomposable direct summands of the motive of a projective -homogeneous
variety with coefficients in remain indecomposable if the ring
of coefficients is any field of characteristic . In particular for any
projective -homogeneous variety , the decomposition of the motive of
in a direct sum of indecomposable motives with coefficients in any finite field
of characteristic corresponds to the decomposition of the motive of
with coefficients in . We also construct a counterexample to this
result in the case where is arbitrary
Prosody as an argument for a layered left periphery
Van Heuven and Haan’s (2000, 2002) experimental work on the prosody of Dutch question types found that the prosodic signalling of interrogativity is stronger for declarative questions, less so for yes/no-questions and even less so for wh-questions. This paper shows how the sequence established on prosodic grounds (declarative questions > yes/no questions > wh questions > statements) is mirrored in the functional hierarchy in syntax. Prosody therefore provides an argument for a detailed left periphery (Rizzi 1997, 2001; Haegeman & Hill 2013)
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