{"issue":"3","abstract":[{"text":"We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n, q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,ℂ)-character variety. The calculation also leads to several conjectures about the cohomology of Mn: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n=2.","lang":"eng"}],"doi":"10.1007/s00222-008-0142-x","author":[{"full_name":"Tamas Hausel","first_name":"Tamas","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"},{"full_name":"Rodríguez Villegas, Fernando","first_name":"Fernando","last_name":"Rodríguez Villegas"}],"year":"2008","acknowledgement":"The first author was supported by NSF grants DMS-0305505 and DMS- 0604775 an Alfred Sloan Fellowship and a Royal Society University Research Fellowship. The second author was supported by an NSF grant DMS-0200605.","page":"555 - 624","oa":1,"type":"journal_article","month":"12","publisher":"Springer","publist_id":"5732","quality_controlled":0,"title":"Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz","citation":{"ieee":"T. Hausel and F. Rodríguez Villegas, “Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz,” <i>Inventiones Mathematicae</i>, vol. 174, no. 3. Springer, pp. 555–624, 2008.","ama":"Hausel T, Rodríguez Villegas F. Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz. <i>Inventiones Mathematicae</i>. 2008;174(3):555-624. doi:<a href=\"https://doi.org/10.1007/s00222-008-0142-x\">10.1007/s00222-008-0142-x</a>","short":"T. Hausel, F. Rodríguez Villegas, Inventiones Mathematicae 174 (2008) 555–624.","ista":"Hausel T, Rodríguez Villegas F. 2008. Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz. Inventiones Mathematicae. 174(3), 555–624.","chicago":"Hausel, Tamás, and Fernando Rodríguez Villegas. “Mixed Hodge Polynomials of Character Varieties: With an Appendix by Nicholas M. Katz.” <i>Inventiones Mathematicae</i>. Springer, 2008. <a href=\"https://doi.org/10.1007/s00222-008-0142-x\">https://doi.org/10.1007/s00222-008-0142-x</a>.","apa":"Hausel, T., &#38; Rodríguez Villegas, F. (2008). Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz. <i>Inventiones Mathematicae</i>. Springer. <a href=\"https://doi.org/10.1007/s00222-008-0142-x\">https://doi.org/10.1007/s00222-008-0142-x</a>","mla":"Hausel, Tamás, and Fernando Rodríguez Villegas. “Mixed Hodge Polynomials of Character Varieties: With an Appendix by Nicholas M. Katz.” <i>Inventiones Mathematicae</i>, vol. 174, no. 3, Springer, 2008, pp. 555–624, doi:<a href=\"https://doi.org/10.1007/s00222-008-0142-x\">10.1007/s00222-008-0142-x</a>."},"intvolume":"       174","date_created":"2018-12-11T11:52:09Z","status":"public","date_published":"2008-12-01T00:00:00Z","date_updated":"2021-01-12T06:50:54Z","day":"01","extern":1,"_id":"1460","publication":"Inventiones Mathematicae","main_file_link":[{"url":"http://arxiv.org/abs/math/0612668","open_access":"1"}],"publication_status":"published","volume":174}