Transcendental Hodge algebra

Expressions of algebra elements and transcendental noncommutative calculus

Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that 1 i~uv in the Weyl algebra is naturally viewed as an indeterminate living in a discrete set N+12 or −(N+12 ) . This may yield a more mathematical understanding of Dirac’s positron theory. A.M.S Classification (2000): Primary 53...

The Hodge Structure on a Filtered Boolean Algebra

Let (Bn) be the order complex of the Boolean algebra and let B(n, k) be the part of (Bn) where all chains have a gap at most k between each set. We give an action of the symmetric group Sl on the l-chains that gives B(n, k) a Hodge structure and decomposes the homology under the action of the Eulerian idempontents. The Sn action on the chains induces an action on the Hodge pieces and we derive ...

Hodge Groups of Hodge Structures with Hodge Numbers

This paper studies the possible Hodge groups of simple polarizable Q-Hodge structures with Hodge numbers (n, 0, . . . , 0, n). In particular, it generalizes earlier work of Ribet and MoonenZarhin to completely determine the possible Hodge groups of such Hodge structures when n is equal to 1, 4, or a prime p. In addition, the paper determines possible Hodge groups, under certain conditions on th...

Hodge loci and absolute Hodge classes

Hidden Hodge symmetries and Hodge correlators

l-adic Étale Theory Hodge Theory Category of l-adic Abelian category MHR Galois modules of real mixed Hodge strucrures Galois group Hodge Galois group GHod := Gal(Q/Q) Galois group of the category MHR Gal(Q/Q) acts on H∗ et(X,Ql), H∗(X(C),R) has a functorial where X is a variety over Q real mixed Hodge structure étale site ?? Gal(Q/Q) acts on the étale site, and thus ?? on categories of étale s...