@PhdThesis{duepublico_mods_00079087, author = {D'Angelo, Alessandro}, title = {Virtual Localization Formula for Witt Theory}, year = {2023}, month = {Oct}, day = {09}, abstract = {In this thesis, we extend the Virtual Localization Formula to a wide class of motivic ring spectra, obtaining in particular a localization formula for virtual fundamental classes in Witt theory KW. We extend to general spectra the notions and operations of equivariant bivariant theories. Then we specialise to SL[$\eta$-1]-oriented spectra A, obtaining a presentations of A(BN) (where N is the normaliser of the torus in SL2), and an Atiyah-Bott localization theorem for AN(X), for X a scheme equipped with an N-action. Of independent interest, we also describe the ring structure of KW(BN) and give a complete computation of KW-valued Euler classes for all rank two vector bundles over BN.}, doi = {10.17185/duepublico/79087}, url = {https://duepublico2.uni-due.de/receive/duepublico_mods_00079087}, url = {https://doi.org/10.17185/duepublico/79087}, file = {:https://duepublico2.uni-due.de/servlets/MCRFileNodeServlet/duepublico_derivate_00078622/Diss_DAngelo.pdf:PDF}, language = {en} }