| , Three formulae for eigenfunctions of integrable Schrodinger operator, Compositio Math. 107 (1997), no. 2, 143--175. |
..... Then for an algebraic correspondence # # CH d (WL L W #,L ) we have an equality of integers Tr (# # # # # : H # (W L , Q # ) deg W t # # W t (# t ) Proof. We show the formula by using log etale cohomology of the closed fiber. Basic references for log etale cohomology are [7] 25] [26] and [17] We regard t as a log scheme with the log structure induced by the standard one on T . The assumption on # means that # acts trivially on the log point t. Let t be a log geometric point over the log point t and W t be the geometric closed fiber. Let H # log (W t , Q # ) be the log etale ....
....t as a log scheme with the log structure induced by the standard one on T . The assumption on # means that # acts trivially on the log point t. Let t be a log geometric point over the log point t and W t be the geometric closed fiber. Let H # log (W t , Q # ) be the log etale cohomology. By [26] Proposition (4.2) there is a canonical isomorphism H # (W L , Q # ) # H # log (W t , Q # ) We fix an isomorphism N r # #(W, MW ) It induces an isomorphism N r # #(W # , MW# ) Let (W T W # ) be the log blow up (W T W # ) # of W T W # studied in Lemma 3.38. It contains ....
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-----, Nearby cycles for log smooth families. Compositio Math. 112 (1998) 45-75.
....the ingredients are in place for the development of obstruction theory for the study of C maps between a free C CW space and a C space, but we leave the task of finding the precise formulation to a reader motivated by specific applications. Local coefficient systems are particularly subtle, see [26]. Next we recall functorial constructions of classifying spaces and C CW approximations (see for instance [4] 21] 34] We will need some of the details later in Section 6. View the ordered set [p] f0; 1; 2; pg as a category, namely, objects are the elements and there is precisely ....
: "A Shapiro lemma for diagrams of spaces with applications to equivariant topology", Compositio Math. 96 (1995), 249-282.
No context found.
, Three formulae for eigenfunctions of integrable Schrodinger operator, Compositio Math. 107 (1997), no. 2, 143--175.
No context found.
-----, Nearby cycles for log smooth families. Compositio Math., 112, (1998) 45-75.
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